SherbyNet - /page/wikibook/entry.mu

Micron Document

<!DOCTYPE html>

<title>Polyhedral map projection</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Polyhedral map projection</span></span>

</h1>

</header>

<p>A <b>polyhedral map projection</b> is a <a href="Map_projection" title="Map projection">map projection</a> based on a <a href="Spherical_polyhedron" title="Spherical polyhedron">spherical polyhedron</a>. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon or other shape in the plane. The best-known polyhedral map projection is <a href="Buckminster_Fuller" title="Buckminster Fuller">Buckminster Fuller</a>'s <a href="Dymaxion_map" title="Dymaxion map">Dymaxion map</a>. When the spherical polyhedron faces are transformed to the faces of an ordinary <a href="Polyhedron" title="Polyhedron">polyhedron</a> instead of laid flat in a plane, the result is a <b>polyhedral globe</b>.<sup id="cite_ref-Pedzich_1-0" class="reference"><a href="#cite_note-Pedzich-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Often the polyhedron used is a <a href="Platonic_solid" title="Platonic solid">Platonic solid</a> or <a href="Archimedean_solid" title="Archimedean solid">Archimedean solid</a>. However, other polyhedra can be used: the <a href="AuthaGraph_projection" title="AuthaGraph projection">AuthaGraph projection</a> makes use of a polyhedron with 96 faces, and the myriahedral projection allows for an arbitrary large number of faces.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

Although <a href="Interruption_(map_projection)" title="Interruption (map projection)">interruptions</a> between faces are common, and more common with an increasing number of faces, some maps avoid them: the <a href="Lee_conformal_projection" class="mw-redirect" title="Lee conformal projection">Lee conformal projection</a> only has interruptions at its border, and the <a href="AuthaGraph_projection" title="AuthaGraph projection">AuthaGraph projection</a> scales its faces so that the map fills a rectangle without internal interruptions. Some projections can be <a href="Tesselate" class="mw-redirect" title="Tesselate">tesselated</a> to fill the plane, the Lee conformal projection among them.

</p><p>To a degree, the polyhedron and the projection used to transform each face of the polyhedron can be considered separately, and some projections can be applied to differently shaped faces. The <a href="Gnomonic_projection" title="Gnomonic projection">gnomonic projection</a> transforms the edges of spherical polyhedra to straight lines, preserving all polyhedra contained within a hemisphere, so it is a common choice. The <a href="Snyder_equal-area_projection" title="Snyder equal-area projection">Snyder equal-area projection</a> can be applied to any polyhedron with regular faces.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The projection used in later versions of the Dymaxion map can be generalized to other equilateral triangular faces,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and even to certain quadrilaterals.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>Polyhedral map projections are useful for creating <a href="Discrete_global_grid" title="Discrete global grid">discrete global grids</a>, as with the <a href="Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">quadrilateralized spherical cube</a> and Icosahedral Snyder Equal Area (ISEA) grids.<sup id="cite_ref-gdggs03_6-0" class="reference"><a href="#cite_note-gdggs03-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>The earliest known polyhedral projection is the <a href="Octant_projection" title="Octant projection">octant projection</a> developed by <a href="Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> or his associate around 1514, which transforms the faces of an <a href="Octahedron" title="Octahedron">octahedron</a> to <a href="Reuleaux_triangle" title="Reuleaux triangle">Reuleaux triangles</a>.<sup id="cite_ref-Pedzich_1-1" class="reference"><a href="#cite_note-Pedzich-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Christian_Gottlieb_Reichard" title="Christian Gottlieb Reichard">Christian Gottlieb Reichard</a> created a polyhedral globe based on the cube in 1803. An icosahedral globe appeared in 1851. Polyhedral globes cheaply constructed from cardboard were popular for a time in Europe.<sup id="cite_ref-Pedzich_1-2" class="reference"><a href="#cite_note-Pedzich-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Projections based on <a href="Dihedra" class="mw-redirect" title="Dihedra">dihedra</a> begin appearing with the <a href="Peirce_quincuncial_projection" title="Peirce quincuncial projection">Peirce quincuncial projection</a> in 1879, <a href="Guyou_hemisphere-in-a-square_projection" title="Guyou hemisphere-in-a-square projection">Guyou hemisphere-in-a-square projection</a> in 1887, and <a href="Adams_hemisphere-in-a-square_projection" title="Adams hemisphere-in-a-square projection">Adams hemisphere-in-a-square projection</a> in 1925. Although the dihedra are not traditional <a href="Polyhedra" class="mw-redirect" title="Polyhedra">polyhedra</a> they are spherical polyhedra, and the methods used in these projections are also used in other polyhedral projections. In the same work as the hemisphere-in-a-square projection, <a href="Oscar_S._Adams" title="Oscar S. Adams">Adams</a> created maps depicting the entire globe in a <a href="Rhombus" title="Rhombus">rhombus</a>, <a href="Hexagon" title="Hexagon">hexagon</a>, and <a href="Hexagram" title="Hexagram">hexagram</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Bernard_J._S._Cahill" title="Bernard J. S. Cahill">Bernard J. S. Cahill</a> invented the "butterfly map", based on the octahedron, in 1909. This was generalized into the <a href="Cahill%E2%80%93Keyes_projection" title="Cahill–Keyes projection">Cahill–Keyes projection</a> in 1975 and the <a href="Waterman_butterfly_projection" title="Waterman butterfly projection">Waterman butterfly projection</a> in 1996. Cahill's work was also influential on Fuller's Dymaxion maps: Fuller's first version, based on a <a href="Cuboctahedron" title="Cuboctahedron">cuboctahedron</a>, was published in 1943, and his second, based on an icosahedron, was published in 1954.<sup id="cite_ref-Pedzich_1-3" class="reference"><a href="#cite_note-Pedzich-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>In 1965, Wellman Chamberlin (also known for his <a href="Chamberlin_trimetric_projection" title="Chamberlin trimetric projection">Chamberlin trimetric projection</a>) and Howard E. Paine of the <a href="National_Geographic_Society" title="National Geographic Society">National Geographic Society</a> designed a polyhedral map based on the 12 equal pentagon faces of a <a href="Dodecahedron" title="Dodecahedron">dodecahedron</a>. 20 years later, Chamberlin and Paine used that polyhedral map in "Global Pursuit", a <a href="Board_game" title="Board game">board game</a> intended to teach geography to children.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>The <a href="Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">quadrilateralized spherical cube</a> was devised in 1975 for the <a href="Cosmic_Background_Explorer" title="Cosmic Background Explorer">Cosmic Background Explorer</a> project.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Gallery">Gallery</h2></div>

<div class="gallerytext"> <a href="Octant_projection" title="Octant projection">Octant projection</a></div>

</li>

<div class="gallerytext"> <a href="Cahill's_butterfly_map" class="mw-redirect" title="Cahill's butterfly map">Cahill's butterfly map</a></div>

</li>

<div class="gallerytext"><a href="Cahill%E2%80%93Keyes_projection" title="Cahill–Keyes projection">Cahill–Keyes projection</a></div>

</li>

<div class="gallerytext"> <a href="Waterman_butterfly_projection" title="Waterman butterfly projection">Waterman butterfly projection</a></div>

</li>

<div class="gallerytext"><a href="Lee_Conformal_Projection" class="mw-redirect" title="Lee Conformal Projection">Lee conformal world on a tetrahedron</a></div>

</li>

<div class="gallerytext"><a href="Peirce_quincuncial_projection" title="Peirce quincuncial projection">Peirce quincuncial</a></div>

</li>

<div class="gallerytext"><a href="Guyou_hemisphere-in-a-square_projection" title="Guyou hemisphere-in-a-square projection">Guyou hemisphere-in-a-square projection</a></div>

</li>

<div class="gallerytext"><a href="Adams_hemisphere-in-a-square_projection" title="Adams hemisphere-in-a-square projection">Adams hemisphere-in-a-square projection</a></div>

</li>

</ul>

<ul><li><a href="HEALPix" title="HEALPix">HEALPix</a>, which is not strictly a polyhedral map projection</li>

<li><a href="List_of_map_projections" title="List of map projections">List of map projections</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFPędzich2016" class="citation journal cs1">Pędzich, Paweł (2016-12-01). <a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fpcr-2016-0014">"Image of the World on polyhedral maps and globes"</a>. <i>Polish Cartographical Review</i>. <b>48</b> (4): <span class="nowrap">197–</span>210. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fpcr-2016-0014">10.1515/pcr-2016-0014</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2450-6966">2450-6966</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:133013421">133013421</a>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFvan_Wijk2008" class="citation journal cs1">van Wijk, Jarke J. (2008). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="http://www.tandfonline.com/doi/full/10.1179/000870408X276594">"Unfolding the Earth: Myriahedral Projections"</a></span>. <i>The Cartographic Journal</i>. <b>45</b> (1): <span class="nowrap">32–</span>42. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1179%2F000870408X276594">10.1179/000870408X276594</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0008-7041">0008-7041</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:218692689">218692689</a>.</cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFSnyder1992" class="citation journal cs1">Snyder, John P (1992-03-01). <a rel="nofollow" class="external text" href="https://utpjournals.press/doi/10.3138/27H7-8K88-4882-1752">"An Equal-Area Map Projection For Polyhedral Globes"</a>. <i>Cartographica: The International Journal for Geographic Information and Geovisualization</i>. <b>29</b> (1): <span class="nowrap">10–</span>21. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3138%2F27H7-8K88-4882-1752">10.3138/27H7-8K88-4882-1752</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0317-7173">0317-7173</a>.</cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFCrider2008" class="citation journal cs1">Crider, John E. (2008-03-01). <a rel="nofollow" class="external text" href="https://utpjournals.press/doi/10.3138/carto.43.1.67">"Exact Equations for Fuller's Map Projection and Inverse"</a>. <i>Cartographica: The International Journal for Geographic Information and Geovisualization</i>. <b>43</b> (1): <span class="nowrap">67–</span>72. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3138%2Fcarto.43.1.67">10.3138/carto.43.1.67</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0317-7173">0317-7173</a>.</cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFCrider2009" class="citation journal cs1">Crider, John E. (2009-01-01). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://doi.org/10.1559/152304009788188781">"A Geodesic Map Projection for Quadrilaterals"</a></span>. <i>Cartography and Geographic Information Science</i>. <b>36</b> (2): <span class="nowrap">131–</span>147. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1559%2F152304009788188781">10.1559/152304009788188781</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1523-0406">1523-0406</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:128390865">128390865</a>.</cite></span>

</li>

<li id="cite_note-gdggs03-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-gdggs03_6-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFSahrWhiteKimerling2003" class="citation journal cs1">Sahr, Kevin; White, Denis; Kimerling, A.J. (2003). <a rel="nofollow" class="external text" href="http://webpages.sou.edu/~sahrk/sqspc/pubs/gdggs03.pdf">"Geodesic discrete global grid systems"</a> <span class="cs1-format">(PDF)</span>. <i>Cartography and Geographic Information Science</i>. <b>30</b> (2): <span class="nowrap">121–</span>134. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1559%2F152304003100011090">10.1559/152304003100011090</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16549179">16549179</a>.</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFAdams1925" class="citation book cs1"><a href="Oscar_S._Adams" title="Oscar S. Adams">Adams, Oscar S.</a> (1925). <a rel="nofollow" class="external text" href="https://geodesy.noaa.gov/library/pdfs/Special_Publication_No_112.pdf"><i>Elliptic Functions Applied to Conformal World Maps</i></a> <span class="cs1-format">(PDF)</span>. United States Coast and Geodetic Survey Special Publication No. 112. U.S. Government Printing Office.</cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFLee1976" class="citation book cs1"><a href="Laurence_Patrick_Lee" title="Laurence Patrick Lee">Lee, L. P.</a> (1976). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/conformalproject0000leel"><i>Conformal Projections Based on Elliptic Functions</i></a></span>. <i>Cartographica Monographs</i>. Vol. 16. Toronto: B. V. Gutsell, York University. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-919870-16-3</bdi>.</cite> Supplement No. 1 to <a rel="nofollow" class="external text" href="https://www.utpjournals.press/toc/cart/13/1"><i>The Canadian Cartographer</i> <b>13</b></a>.</span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite id="CITEREFScheel2002" class="citation news cs1">Scheel, Eugene (May 19, 2002). <a rel="nofollow" class="external text" href="https://www.washingtonpost.com/archive/local/2002/05/19/with-intellect-and-artistry-wellman-chamberlin-created-a-world-of-his-own/627dbea8-370a-4b16-83cd-46e6388a9dfb/">"With Intellect and Artistry, Wellman Chamberlin Created a World of His Own"</a>. <i>The Washington Post</i>.</cite></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://boardgamegeek.com/boardgame/3676/global-pursuit">"Global Pursuit (1987)"</a>. <i>BoardGameGeek</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-08-30</span></span>.</cite></span>

</li>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFChanO'Neill1975" class="citation techreport cs1">Chan, F.K.; O'Neill, E. M. (1975). <a rel="nofollow" class="external text" href="https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA010232.xhtml"><i>Feasibility Study of a Quadrilateralized Spherical Cube Earth Data Base (CSC - Computer Sciences Corporation, EPRF Technical Report 2-75)</i></a> (Technical report). Monterey, California: Environmental Prediction Research Facility.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite id="CITEREFO'Neill1976" class="citation techreport cs1">O'Neill, E. M. (1976). <a rel="nofollow" class="external text" href="https://apps.dtic.mil/dtic/tr/fulltext/u2/a026294.pdf"><i>Extended Studies of a Quadrilateralized Spherical Cube Earth Data Base</i></a> <span class="cs1-format">(PDF)</span> (Technical report). Monterey, California: Environmental Prediction Research Facility. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190507002144/https://apps.dtic.mil/dtic/tr/fulltext/u2/a026294.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on May 7, 2019.</cite></span>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://philogb.github.io/page/myriahedral/">Unfolding the Earth: Myriahedral Projections</a> — an interactive visualization of myriahedral projections.</li></ul>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1236075235">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox" aria-labelledby="Map_projection114" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><style data-mw-deduplicate="TemplateStyles:r1239400231">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div id="Map_projection114" style="font-size:114%;margin:0 4em"><a href="Map_projection" title="Map projection">Map projection</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><a href="History_of_cartography" title="History of cartography">History</a></li>

<li><a href="Portal%3AMaps" title="Portal:Maps">Portal</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_surface114" style="font-size:114%;margin:0 4em"><a href="Map_projection#Projections_by_surface" title="Map projection">By surface</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Cylindrical" title="Map projection">Cylindrical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="Mercator_projection" title="Mercator projection">Mercator</a>-conformal</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Gauss%E2%80%93Kr%C3%BCger_coordinate_system" class="mw-redirect" title="Gauss–Krüger coordinate system">Gauss–Krüger</a></li>

<li><a href="Transverse_Mercator_projection" title="Transverse Mercator projection">Transverse Mercator</a></li>

<li><a href="Oblique_Mercator_projection" title="Oblique Mercator projection">Oblique Mercator</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="Cylindrical_equal-area_projection" title="Cylindrical equal-area projection">Equal-area</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Balthasart</a></li>

<li><a href="Behrmann_projection" title="Behrmann projection">Behrmann</a></li>

<li><a href="Gall%E2%80%93Peters_projection" title="Gall–Peters projection">Gall–Peters</a></li>

<li><a href="Lambert_cylindrical_equal-area_projection" title="Lambert cylindrical equal-area projection">Lambert</a></li>

<li><a href="Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Smyth equal-surface</a></li>

<li><a href="Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Trystan Edwards</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cassini_projection" title="Cassini projection">Cassini</a></li>

<li><a href="Central_cylindrical_projection" title="Central cylindrical projection">Central</a></li>

<li><a href="Equirectangular_projection" title="Equirectangular projection">Equirectangular</a></li>

<li><a href="Gall_stereographic_projection" title="Gall stereographic projection">Gall stereographic</a></li>

<li><a href="Gall_isographic_projection" title="Gall isographic projection">Gall isographic</a></li>

<li><a href="Miller_cylindrical_projection" title="Miller cylindrical projection">Miller</a></li>

<li><a href="Space-oblique_Mercator_projection" title="Space-oblique Mercator projection">Space-oblique Mercator</a></li>

<li><a href="Web_Mercator_projection" title="Web Mercator projection">Web Mercator</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Pseudocylindrical" title="Map projection">Pseudocylindrical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Equal-area10" scope="row" class="navbox-group" style="width:1%">Equal-area</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Collignon_projection" title="Collignon projection">Collignon</a></li>

<li><a href="Eckert_II_projection" title="Eckert II projection">Eckert II</a></li>

<li><a href="Eckert_IV_projection" title="Eckert IV projection">Eckert IV</a></li>

<li><a href="Eckert_VI_projection" title="Eckert VI projection">Eckert VI</a></li>

<li><a href="Equal_Earth_projection" title="Equal Earth projection">Equal Earth</a></li>

<li><a href="Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li>

<li><a href="Mollweide_projection" title="Mollweide projection">Mollweide</a></li>

<li><a href="Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>

<li><a href="Tobler_hyperelliptical_projection" title="Tobler hyperelliptical projection">Tobler hyperelliptical</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Kavrayskiy_VII_projection" title="Kavrayskiy VII projection">Kavrayskiy VII</a></li>

<li><a href="Wagner_VI_projection" title="Wagner VI projection">Wagner VI</a></li>

<li><a href="Winkel_projection" title="Winkel projection">Winkel I and II</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Conical" title="Map projection">Conical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Albers_projection" title="Albers projection">Albers</a></li>

<li><a href="Equidistant_conic_projection" title="Equidistant conic projection">Equidistant</a></li>

<li><a href="Lambert_conformal_conic_projection" title="Lambert conformal conic projection">Lambert conformal</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Pseudoconical" title="Map projection">Pseudoconical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bonne_projection" title="Bonne projection">Bonne</a></li>

<li><a href="Bottomley_projection" title="Bottomley projection">Bottomley</a></li>

<li><a href="Polyconic_projection_class" title="Polyconic projection class">Polyconic</a>

<ul><li><a href="American_polyconic_projection" title="American polyconic projection">American</a></li>

<li><a href="Latitudinally_equal-differential_polyconic_projection" title="Latitudinally equal-differential polyconic projection">Chinese</a></li></ul></li>

<li><a href="Werner_projection" title="Werner projection">Werner</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Azimuthal" title="Map projection">Azimuthal<br><span class="nobold">(planar)</span></a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="General_perspective54" scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="General_Perspective_projection" title="General Perspective projection">General perspective</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li>

<li><a href="Orthographic_map_projection" title="Orthographic map projection">Orthographic</a></li>

<li><a href="Stereographic_map_projection" title="Stereographic map projection">Stereographic</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Azimuthal_equidistant_projection" title="Azimuthal equidistant projection">Equidistant</a></li>

<li><a href="Lambert_azimuthal_equal-area_projection" title="Lambert azimuthal equal-area projection">Lambert equal-area</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Pseudoazimuthal" title="Map projection">Pseudoazimuthal</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aitoff_projection" title="Aitoff projection">Aitoff</a></li>

<li><a href="Hammer_projection" title="Hammer projection">Hammer</a></li>

<li><a href="Wiechel_projection" title="Wiechel projection">Wiechel</a></li>

<li><a href="Winkel_tripel_projection" title="Winkel tripel projection">Winkel tripel</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_metric114" style="font-size:114%;margin:0 4em"><a href="Map_projection#Projections_by_preservation_of_a_metric_property" title="Map projection">By metric</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Conformal_map_projection" title="Conformal map projection">Conformal</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Adams_hemisphere-in-a-square_projection" title="Adams hemisphere-in-a-square projection">Adams hemisphere-in-a-square</a></li>

<li><a href="Gauss%E2%80%93Kr%C3%BCger_coordinate_system" class="mw-redirect" title="Gauss–Krüger coordinate system">Gauss–Krüger</a></li>

<li><a href="Guyou_hemisphere-in-a-square_projection" title="Guyou hemisphere-in-a-square projection">Guyou hemisphere-in-a-square</a></li>

<li><a href="Lambert_conformal_conic_projection" title="Lambert conformal conic projection">Lambert conformal conic</a></li>

<li><a href="Mercator_projection" title="Mercator projection">Mercator</a></li>

<li><a href="Peirce_quincuncial_projection" title="Peirce quincuncial projection">Peirce quincuncial</a></li>

<li><a href="Stereographic_projection" title="Stereographic projection">Stereographic</a></li>

<li><a href="Transverse_Mercator_projection" title="Transverse Mercator projection">Transverse Mercator</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Equal-area_projection" title="Equal-area projection">Equal-area</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="Bonne_projection" title="Bonne projection">Bonne</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>

<li><a href="Werner_projection" title="Werner projection">Werner</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="Bottomley_projection" title="Bottomley projection">Bottomley</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>

<li><a href="Werner_projection" title="Werner projection">Werner</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="Cylindrical_equal-area_projection" title="Cylindrical equal-area projection">Cylindrical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Balthasart</a></li>

<li><a href="Behrmann_projection" title="Behrmann projection">Behrmann</a></li>

<li><a href="Gall%E2%80%93Peters_projection" title="Gall–Peters projection">Gall–Peters</a></li>

<li><a href="Lambert_cylindrical_equal-area_projection" title="Lambert cylindrical equal-area projection">Lambert cylindrical equal-area</a></li>

<li><a href="Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Smyth equal-surface</a></li>

<li><a href="Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Trystan Edwards</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="Tobler_hyperelliptical_projection" title="Tobler hyperelliptical projection">Tobler hyperelliptical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Collignon_projection" title="Collignon projection">Collignon</a></li>

<li><a href="Mollweide_projection" title="Mollweide projection">Mollweide</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Albers_projection" title="Albers projection">Albers</a></li>

<li><a href="Hammer_projection#Briesemeister" title="Hammer projection">Briesemeister</a></li>

<li><a href="Eckert_II_projection" title="Eckert II projection">Eckert II</a></li>

<li><a href="Eckert_IV_projection" title="Eckert IV projection">Eckert IV</a></li>

<li><a href="Eckert_VI_projection" title="Eckert VI projection">Eckert VI</a></li>

<li><a href="Equal_Earth_projection" title="Equal Earth projection">Equal Earth</a></li>

<li><a href="Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li>

<li><a href="Hammer_projection" title="Hammer projection">Hammer</a></li>

<li><a href="Lambert_azimuthal_equal-area_projection" title="Lambert azimuthal equal-area projection">Lambert azimuthal equal-area</a></li>

<li><a href="Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">Quadrilateralized spherical cube</a></li>

<li><a href="Strebe_1995_projection" title="Strebe 1995 projection">Strebe 1995</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Equidistant" title="Map projection">Equidistant in<br>some aspect</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Equidistant_conic_projection" title="Equidistant conic projection">Conic</a></li>

<li><a href="Equirectangular_projection" title="Equirectangular projection">Equirectangular</a></li>

<li><a href="Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>

<li><a href="Two-point_equidistant_projection" title="Two-point equidistant projection">Two-point</a></li>

<li><a href="Werner_projection" title="Werner projection">Werner</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Gnomonic" title="Map projection">Gnomonic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Rhumb_line" title="Map projection">Loxodromic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Loximuthal_projection" title="Loximuthal projection">Loximuthal</a></li>

<li><a href="Mercator_projection" title="Mercator projection">Mercator</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Retroazimuthal" title="Map projection">Retroazimuthal</a><br><span class="nobold">(Mecca or Qibla)</span></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Craig_retroazimuthal_projection" title="Craig retroazimuthal projection">Craig</a></li>

<li><a href="Hammer_retroazimuthal_projection" title="Hammer retroazimuthal projection">Hammer</a></li>

<li><a href="Littrow_projection" title="Littrow projection">Littrow</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_construction114" style="font-size:114%;margin:0 4em"><a href="Map_projection#Classification" title="Map projection">By construction</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Compromise_projections" title="Map projection">Compromise</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Chamberlin_trimetric_projection" title="Chamberlin trimetric projection">Chamberlin trimetric</a></li>

<li><a href="Kavrayskiy_VII_projection" title="Kavrayskiy VII projection">Kavrayskiy VII</a></li>

<li><a href="Miller_cylindrical_projection" title="Miller cylindrical projection">Miller cylindrical</a></li>

<li><a href="Natural_Earth_projection" title="Natural Earth projection">Natural Earth</a></li>

<li><a href="Robinson_projection" title="Robinson projection">Robinson</a></li>

<li><a href="Van_der_Grinten_projection" title="Van der Grinten projection">Van der Grinten</a></li>

<li><a href="Wagner_VI_projection" title="Wagner VI projection">Wagner VI</a></li>

<li><a href="Winkel_tripel_projection" title="Winkel tripel projection">Winkel tripel</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Hybrid" title="Map projection">Hybrid</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li>

<li><a href="HEALPix" title="HEALPix">HEALPix</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Perspective_projections" title="Map projection">Perspective</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Planar41" scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="General_Perspective_projection" title="General Perspective projection">Planar</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li>

<li><a href="Orthographic_map_projection" title="Orthographic map projection">Orthographic</a></li>

<li><a href="Stereographic_projection" title="Stereographic projection">Stereographic</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Central_cylindrical_projection" title="Central cylindrical projection">Central cylindrical</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Map_projection#Polyhedral" title="Map projection">Polyhedral</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="AuthaGraph_projection" title="AuthaGraph projection">AuthaGraph</a></li>

<li><a href="Bernard_J._S._Cahill" title="Bernard J. S. Cahill">Cahill Butterfly</a></li>

<li><a href="Cahill%E2%80%93Keyes_projection" title="Cahill–Keyes projection">Cahill–Keyes M-shape</a></li>

<li><a href="Dymaxion_map" title="Dymaxion map">Dymaxion</a></li>

<li><a href="Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">Quadrilateralized spherical cube</a></li>

<li><a href="Waterman_butterfly_projection" title="Waterman butterfly projection">Waterman butterfly</a></li></ul>

<ul><li><a href="Interruption_(map_projection)" title="Interruption (map projection)">Interruption (map projection)</a></li>

<li><a href="Latitude" title="Latitude">Latitude</a></li>

<li><a href="Longitude" title="Longitude">Longitude</a></li>

<li><a href="Tissot's_indicatrix" title="Tissot's indicatrix">Tissot's indicatrix</a></li>

<li><a href="Map_projection_of_the_tri-axial_ellipsoid" class="mw-redirect" title="Map projection of the tri-axial ellipsoid">Map projection of the tri-axial ellipsoid</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-06-24" href="https://en.wikipedia.org/wiki/?title=Polyhedral_map_projection&oldid=1297134736">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>