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<title>Augmented triangular prism</title>

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</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above" style="background:#e7dcc3">Augmented triangular prism</th></tr><tr><td colspan="2" class="infobox-image"></td></tr><tr><th scope="row" class="infobox-label">Type</th><td class="infobox-data"><a href="Johnson_solid" title="Johnson solid">Johnson</a><br><span class="texhtml"><a href="Gyroelongated_pentagonal_birotunda" title="Gyroelongated pentagonal birotunda"><i>J</i><sub>48</sub></a> – <b><i>J</i><sub>49</sub></b> – <a href="Biaugmented_triangular_prism" title="Biaugmented triangular prism"><i>J</i><sub>50</sub></a></span></td></tr><tr><th scope="row" class="infobox-label"><a href="Face_(geometry)" title="Face (geometry)">Faces</a></th><td class="infobox-data">6 <a href="Triangle" title="Triangle">triangles</a><br>2 <a href="Square_(geometry)" class="mw-redirect" title="Square (geometry)">squares</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Edge_(geometry)" title="Edge (geometry)">Edges</a></th><td class="infobox-data">13</td></tr><tr><th scope="row" class="infobox-label"><a href="Vertex_(geometry)" title="Vertex (geometry)">Vertices</a></th><td class="infobox-data">7</td></tr><tr><th scope="row" class="infobox-label"><a href="Vertex_configuration" title="Vertex configuration">Vertex configuration</a></th><td class="infobox-data"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}&2\times (3\times 4^{2})\,+\\&1\times (3^{4})\,+\\&4\times (3^{3}\times 4)\end{aligned}}}">

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</math></span><img src="./4fb030812a1d9e1bf76a6fa6a0b6d03578fc10b5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:14.978ex; height:9.843ex;" alt="{\displaystyle {\begin{aligned}&2\times (3\times 4^{2})\,+\\&1\times (3^{4})\,+\\&4\times (3^{3}\times 4)\end{aligned}}}" loading="lazy"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry group</a></th><td class="infobox-data"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{2\mathrm {v} }}">

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</math></span><img src="./3f9709f679aa6eaf1ea557c648c5f0fe4bd23c23.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.584ex; height:2.509ex;" alt="{\displaystyle C_{2\mathrm {v} }}" loading="lazy"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="Dihedral_angle" title="Dihedral angle">Dihedral angle</a> (<a href="Degree_(angle)" title="Degree (angle)">degrees</a>)</th><td class="infobox-data">triangle-triangle: 109.5°, 169.4°<br>triangle-square: 90°, 114.7°<br>square-square: 60°</td></tr><tr><th scope="row" class="infobox-label">Properties</th><td class="infobox-data"><a href="Convex_polyhedron" class="mw-redirect" title="Convex polyhedron">convex</a>, <a href="Composite_polyhedron" title="Composite polyhedron">composite</a></td></tr><tr><th colspan="2" class="infobox-header" style="background:#e7dcc3"><a href="Net_(polyhedron)" title="Net (polyhedron)">Net</a></th></tr><tr><td colspan="2" class="infobox-full-data"></td></tr></tbody></table>

<p>In <a href="Geometry" title="Geometry">geometry</a>, the <b>augmented triangular prism</b> is a polyhedron constructed by attaching an <a href="Equilateral_square_pyramid" class="mw-redirect" title="Equilateral square pyramid">equilateral square pyramid</a> onto the square face of a <a href="Triangular_prism" title="Triangular prism">triangular prism</a>. As a result, it is an example of <a href="Johnson_solid" title="Johnson solid">Johnson solid</a>. It can be visualized as the chemical compound, known as <a href="Capped_trigonal_prismatic_molecular_geometry" title="Capped trigonal prismatic molecular geometry">capped trigonal prismatic molecular geometry</a>.

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

<p>The augmented triangular prism is <a href="Composite_polyhedron" title="Composite polyhedron">composite</a>: it can be constructed from a <a href="Triangular_prism" title="Triangular prism">triangular prism</a> by attaching an <a href="Equilateral_square_pyramid" class="mw-redirect" title="Equilateral square pyramid">equilateral square pyramid</a> to one of its square faces, a process known as <a href="Augmentation_(geometry)" class="mw-redirect" title="Augmentation (geometry)">augmentation</a>.<sup id="cite_ref-timofeenko-2009_1-0" class="reference"><a href="#cite_note-timofeenko-2009-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-rajwade_2-0" class="reference"><a href="#cite_note-rajwade-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> This square pyramid covers the square face of the prism, so the resulting polyhedron has six <a href="Equilateral_triangle" title="Equilateral triangle">equilateral triangles</a> and two <a href="Square_(geometry)" class="mw-redirect" title="Square (geometry)">squares</a> as its faces.<sup id="cite_ref-berman_3-0" class="reference"><a href="#cite_note-berman-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> A <a href="Convex_set" title="Convex set">convex</a> polyhedron in which all faces are <a href="Regular_polygon" title="Regular polygon">regular</a> is <a href="Johnson_solid" title="Johnson solid">Johnson solid</a>. The augmented triangular prism is among them, enumerated as the forty-ninth Johnson solid <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J_{49}}">

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</math></span><img src="./c4d605933a376de528e8626b530664f253fade9d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.166ex; height:2.509ex;" alt="{\displaystyle J_{49}}" loading="lazy"></span>.<sup id="cite_ref-francis_4-0" class="reference"><a href="#cite_note-francis-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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

<p>An augmented triangular prism with edge length <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}">

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Its volume can be obtained by slicing it into a regular triangular prism and an equilateral square pyramid, and adding their volume subsequently:<sup id="cite_ref-berman_3-2" class="reference"><a href="#cite_note-berman-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {2{\sqrt {2}}+3{\sqrt {3}}}{12}}a^{3}\approx 0.669a^{3}.}</annotation>

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</p><p>It has <a href="Point_groups_in_three_dimensions" title="Point groups in three dimensions">three-dimensional symmetry group</a> of the cyclic group <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{2\mathrm {v} }}">

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<ul><li>The dihedral angle of an augmented triangular prism between two adjacent triangles is that of an equilateral square pyramid between two adjacent triangular faces, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \arccos \left(-1/3\right)\approx 109.5^{\circ }}">

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<annotation encoding="application/x-tex">{\textstyle \arccos \left(-1/3\right)\approx 109.5^{\circ }}</annotation>

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<li>The dihedral angle of an augmented triangular prism between two adjacent squares is that of a triangular prism between two lateral faces, the <a href="Interior_angle" class="mw-redirect" title="Interior angle">interior angle</a> of a triangular prism <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi /3=60^{\circ }}">

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<annotation encoding="application/x-tex">{\displaystyle \pi /3=60^{\circ }}</annotation>

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</math></span><img src="./fd5c425ced9b2cc03700f42d345c42c570e8fc80.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.135ex; height:2.843ex;" alt="{\displaystyle \pi /3=60^{\circ }}" loading="lazy"></span>.</li>

<li>The dihedral angle of an augmented triangular prism between square and triangle is the dihedral angle of a triangular prism between the base and its lateral face, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \pi /2=90^{\circ }}">

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</math></span><img src="./7cdfca69fd65df7eadb57c4edd1327f265dc9104.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.135ex; height:2.843ex;" alt="{\textstyle \pi /2=90^{\circ }}" loading="lazy"></span></li>

<li>The dihedral angle of an equilateral square pyramid between a triangular face and its base is <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \arctan \left({\sqrt {2}}\right)\approx 54.7^{\circ }}">

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<annotation encoding="application/x-tex">{\textstyle \arctan \left({\sqrt {2}}\right)\approx 54.7^{\circ }}</annotation>

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</math></span><img src="./d938ddf111711434fe1700c00f0c7f44577e50f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.981ex; height:3.343ex;" alt="{\textstyle \arctan \left({\sqrt {2}}\right)\approx 54.7^{\circ }}" loading="lazy"></span>. Therefore, the dihedral angle of an augmented triangular prism between a square (the lateral face of the triangular prism) and triangle (the lateral face of the equilateral square pyramid) on the edge where the equilateral square pyramid is attached to the square face of the triangular prism, and between two adjacent triangles (the lateral face of both equilateral square pyramids) on the edge where two equilateral square pyramids are attached adjacently to the triangular prism, are <span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\arctan \left({\sqrt {2}}\right)+{\frac {\pi }{3}}&\approx 114.7^{\circ },\\2\arctan \left({\sqrt {2}}\right)+{\frac {\pi }{3}}&\approx 169.4^{\circ }.\end{aligned}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\arctan \left({\sqrt {2}}\right)+{\frac {\pi }{3}}&\approx 114.7^{\circ },\\2\arctan \left({\sqrt {2}}\right)+{\frac {\pi }{3}}&\approx 169.4^{\circ }.\end{aligned}}}</annotation>

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

<p>In the geometry of <a href="Chemical_compounds" class="mw-redirect" title="Chemical compounds">chemical compounds</a>, a polyhedron may commonly be visualized an <a href="Atom_cluster" class="mw-redirect" title="Atom cluster">atom cluster</a> surrounding a central atom. The <a href="Capped_trigonal_prismatic_molecular_geometry" title="Capped trigonal prismatic molecular geometry">capped trigonal prismatic molecular geometry</a> describes clusters for which this polyhedron is an augmented triangular prism.<sup id="cite_ref-hbmr_6-0" class="reference"><a href="#cite_note-hbmr-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> An example of such compound is the <a href="Potassium_heptafluorotantalate" title="Potassium heptafluorotantalate">potassium heptafluorotantalate</a>.<sup id="cite_ref-kaupp_7-0" class="reference"><a href="#cite_note-kaupp-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

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<ul><li><a href="Biaugmented_triangular_prism" title="Biaugmented triangular prism">Biaugmented triangular prism</a> — the 50th Johnson solid, constructed by attaching a triangular prism to two equilateral square pyramids.</li>

<li><a href="Triaugmented_triangular_prism" title="Triaugmented triangular prism">Triaugmented triangular prism</a> — the 51st Johnson solid, constructed by augmenting each square face of a triangular prism with a square pyramid.</li></ul>

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

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</style><cite id="CITEREFTimofeenko2009" class="citation journal cs1">Timofeenko, A. V. (2009). <a rel="nofollow" class="external text" href="https://www.interocitors.com/tmp/papers/timo-parquet.pdf">"Convex Polyhedra with Parquet Faces"</a> <span class="cs1-format">(PDF)</span>. <i>Docklady Mathematics</i>. <b>80</b> (2): <span class="nowrap">720–</span>723. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1134%2FS1064562409050238">10.1134/S1064562409050238</a>.</cite></span>

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<li id="cite_note-rajwade-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-rajwade_2-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFRajwade2001" class="citation book cs1">Rajwade, A. R. (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=afJdDwAAQBAJ&pg=PA84"><i>Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem</i></a>. Texts and Readings in Mathematics. Hindustan Book Agency. p. 84–89. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-93-86279-06-4">10.1007/978-93-86279-06-4</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-93-86279-06-4</bdi>.</cite></span>

</li>

<li id="cite_note-berman-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-berman_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-berman_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-berman_3-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFBerman1971" class="citation journal cs1">Berman, Martin (1971). "Regular-faced convex polyhedra". <i>Journal of the Franklin Institute</i>. <b>291</b> (5): <span class="nowrap">329–</span>352. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0016-0032%2871%2990071-8">10.1016/0016-0032(71)90071-8</a>. <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0290245">0290245</a>.</cite></span>

</li>

<li id="cite_note-francis-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-francis_4-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFFrancis2013" class="citation journal cs1">Francis, Darryl (August 2013). <a rel="nofollow" class="external text" href="https://go.gale.com/ps/i.do?id=GALE%7CA340298118">"Johnson solids & their acronyms"</a>. <i>Word Ways</i>. <b>46</b> (3): 177.</cite></span>

</li>

<li id="cite_note-johnson-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-johnson_5-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFJohnson1966" class="citation journal cs1"><a href="Norman_W._Johnson" class="mw-redirect" title="Norman W. Johnson">Johnson, Norman W.</a> (1966). <a rel="nofollow" class="external text" href="https://doi.org/10.4153%2Fcjm-1966-021-8">"Convex polyhedra with regular faces"</a>. <i><a href="Canadian_Journal_of_Mathematics" title="Canadian Journal of Mathematics">Canadian Journal of Mathematics</a></i>. <b>18</b>: <span class="nowrap">169–</span>200. <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/10.4153%2Fcjm-1966-021-8">10.4153/cjm-1966-021-8</a></span>. <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0185507">0185507</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:122006114">122006114</a>. <a href="Zbl_(identifier)" class="mw-redirect" title="Zbl (identifier)">Zbl</a> <a rel="nofollow" class="external text" href="https://zbmath.org/?format=complete&q=an:0132.14603">0132.14603</a>.</cite></span>

</li>

<li id="cite_note-hbmr-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-hbmr_6-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFHoffmannBeierMuettertiesRossi1977" class="citation journal cs1">Hoffmann, Roald; Beier, Barbara F.; Muetterties, Earl L.; Rossi, Angelo R. (1977). "Seven-coordination. A molecular orbital exploration of structure, stereochemistry, and reaction dynamics". <i><a href="Inorganic_Chemistry_(journal)" title="Inorganic Chemistry (journal)">Inorganic Chemistry</a></i>. <b>16</b> (3): <span class="nowrap">511–</span>522. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fic50169a002">10.1021/ic50169a002</a>.</cite></span>

</li>

<li id="cite_note-kaupp-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-kaupp_7-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFKaupp2001" class="citation journal cs1">Kaupp, Martin (2001). ""Non-VSEPR" Structures and Bonding in d(0) Systems". <i>Angew Chem Int Ed Engl</i>. <b>40</b> (1): <span class="nowrap">3534–</span>3565. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F1521-3773%2820011001%2940%3A19%3C3534%3A%3AAID-ANIE3534%3E3.0.CO%3B2-%23">10.1002/1521-3773(20011001)40:19<3534::AID-ANIE3534>3.0.CO;2-#</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11592184">11592184</a>.</cite></span>

</li>

</ol></div></div>

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

<ul><li><span class="citation mathworld" id="Reference-Mathworld-Johnson_Solid"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/JohnsonSolid.html">"Johnson Solid"</a>. <i><a href="MathWorld" title="MathWorld">MathWorld</a></i>.</cite></span>

<ul><li><span class="citation mathworld" id="Reference-Mathworld-Augmented_triangular_prism"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/AugmentedTriangularPrism.html">"Augmented triangular prism"</a>. <i><a href="MathWorld" title="MathWorld">MathWorld</a></i>.</cite></span></li></ul></li></ul>

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</style><div id="Johnson_solids430" style="font-size:114%;margin:0 4em"><a href="Johnson_solid" title="Johnson solid">Johnson solids</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Pyramid_(geometry)" title="Pyramid (geometry)">Pyramids</a>, <a href="Cupola_(geometry)" title="Cupola (geometry)">cupolae</a> and <a href="Rotunda_(geometry)" title="Rotunda (geometry)">rotundae</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Square_pyramid" title="Square pyramid">square pyramid</a></li>

<li><a href="Pentagonal_pyramid" title="Pentagonal pyramid">pentagonal pyramid</a></li>

<li><a href="Triangular_cupola" title="Triangular cupola">triangular cupola</a></li>

<li><a href="Square_cupola" title="Square cupola">square cupola</a></li>

<li><a href="Pentagonal_cupola" title="Pentagonal cupola">pentagonal cupola</a></li>

<li><a href="Pentagonal_rotunda" title="Pentagonal rotunda">pentagonal rotunda</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modified <a href="Pyramid_(geometry)" title="Pyramid (geometry)">pyramids</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Elongated_triangular_pyramid" title="Elongated triangular pyramid">elongated triangular pyramid</a></li>

<li><a href="Elongated_square_pyramid" title="Elongated square pyramid">elongated square pyramid</a></li>

<li><a href="Elongated_pentagonal_pyramid" title="Elongated pentagonal pyramid">elongated pentagonal pyramid</a></li>

<li><a href="Gyroelongated_square_pyramid" title="Gyroelongated square pyramid">gyroelongated square pyramid</a></li>

<li><a href="Gyroelongated_pentagonal_pyramid" title="Gyroelongated pentagonal pyramid">gyroelongated pentagonal pyramid</a></li>

<li><a href="Triangular_bipyramid" title="Triangular bipyramid">triangular bipyramid</a></li>

<li><a href="Pentagonal_bipyramid" title="Pentagonal bipyramid">pentagonal bipyramid</a></li>

<li><a href="Elongated_triangular_bipyramid" title="Elongated triangular bipyramid">elongated triangular bipyramid</a></li>

<li><a href="Elongated_square_bipyramid" title="Elongated square bipyramid">elongated square bipyramid</a></li>

<li><a href="Elongated_pentagonal_bipyramid" title="Elongated pentagonal bipyramid">elongated pentagonal bipyramid</a></li>

<li><a href="Gyroelongated_square_bipyramid" title="Gyroelongated square bipyramid">gyroelongated square bipyramid</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modified <a href="Cupola_(geometry)" title="Cupola (geometry)">cupolae</a> and <a href="Rotunda_(geometry)" title="Rotunda (geometry)">rotundae</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Elongated_triangular_cupola" title="Elongated triangular cupola">elongated triangular cupola</a></li>

<li><a href="Elongated_square_cupola" title="Elongated square cupola">elongated square cupola</a></li>

<li><a href="Elongated_pentagonal_cupola" title="Elongated pentagonal cupola">elongated pentagonal cupola</a></li>

<li><a href="Elongated_pentagonal_rotunda" title="Elongated pentagonal rotunda">elongated pentagonal rotunda</a></li>

<li><a href="Gyroelongated_triangular_cupola" title="Gyroelongated triangular cupola">gyroelongated triangular cupola</a></li>

<li><a href="Gyroelongated_square_cupola" title="Gyroelongated square cupola">gyroelongated square cupola</a></li>

<li><a href="Gyroelongated_pentagonal_cupola" title="Gyroelongated pentagonal cupola">gyroelongated pentagonal cupola</a></li>

<li><a href="Gyroelongated_pentagonal_rotunda" title="Gyroelongated pentagonal rotunda">gyroelongated pentagonal rotunda</a></li>

<li><a href="Gyrobifastigium" title="Gyrobifastigium">gyrobifastigium</a></li>

<li><a href="Triangular_orthobicupola" title="Triangular orthobicupola">triangular orthobicupola</a></li>

<li><a href="Square_orthobicupola" title="Square orthobicupola">square orthobicupola</a></li>

<li><a href="Square_gyrobicupola" title="Square gyrobicupola">square gyrobicupola</a></li>

<li><a href="Pentagonal_orthobicupola" title="Pentagonal orthobicupola">pentagonal orthobicupola</a></li>

<li><a href="Pentagonal_gyrobicupola" title="Pentagonal gyrobicupola">pentagonal gyrobicupola</a></li>

<li><a href="Pentagonal_orthocupolarotunda" title="Pentagonal orthocupolarotunda">pentagonal orthocupolarotunda</a></li>

<li><a href="Pentagonal_gyrocupolarotunda" title="Pentagonal gyrocupolarotunda">pentagonal gyrocupolarotunda</a></li>

<li><a href="Pentagonal_orthobirotunda" title="Pentagonal orthobirotunda">pentagonal orthobirotunda</a></li>

<li><a href="Elongated_triangular_orthobicupola" title="Elongated triangular orthobicupola">elongated triangular orthobicupola</a></li>

<li><a href="Elongated_triangular_gyrobicupola" title="Elongated triangular gyrobicupola">elongated triangular gyrobicupola</a></li>

<li><a href="Elongated_square_gyrobicupola" title="Elongated square gyrobicupola">elongated square gyrobicupola</a></li>

<li><a href="Elongated_pentagonal_orthobicupola" title="Elongated pentagonal orthobicupola">elongated pentagonal orthobicupola</a></li>

<li><a href="Elongated_pentagonal_gyrobicupola" title="Elongated pentagonal gyrobicupola">elongated pentagonal gyrobicupola</a></li>

<li><a href="Elongated_pentagonal_orthocupolarotunda" title="Elongated pentagonal orthocupolarotunda">elongated pentagonal orthocupolarotunda</a></li>

<li><a href="Elongated_pentagonal_gyrocupolarotunda" title="Elongated pentagonal gyrocupolarotunda">elongated pentagonal gyrocupolarotunda</a></li>

<li><a href="Elongated_pentagonal_orthobirotunda" title="Elongated pentagonal orthobirotunda">elongated pentagonal orthobirotunda</a></li>

<li><a href="Elongated_pentagonal_gyrobirotunda" title="Elongated pentagonal gyrobirotunda">elongated pentagonal gyrobirotunda</a></li>

<li><a href="Gyroelongated_triangular_bicupola" title="Gyroelongated triangular bicupola">gyroelongated triangular bicupola</a></li>

<li><a href="Gyroelongated_square_bicupola" title="Gyroelongated square bicupola">gyroelongated square bicupola</a></li>

<li><a href="Gyroelongated_pentagonal_bicupola" title="Gyroelongated pentagonal bicupola">gyroelongated pentagonal bicupola</a></li>

<li><a href="Gyroelongated_pentagonal_cupolarotunda" title="Gyroelongated pentagonal cupolarotunda">gyroelongated pentagonal cupolarotunda</a></li>

<li><a href="Gyroelongated_pentagonal_birotunda" title="Gyroelongated pentagonal birotunda">gyroelongated pentagonal birotunda</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Augmented <a href="Prism_(geometry)" title="Prism (geometry)">prisms</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul>

<li><a href="Biaugmented_triangular_prism" title="Biaugmented triangular prism">biaugmented triangular prism</a></li>

<li><a href="Triaugmented_triangular_prism" title="Triaugmented triangular prism">triaugmented triangular prism</a></li>

<li><a href="Augmented_pentagonal_prism" title="Augmented pentagonal prism">augmented pentagonal prism</a></li>

<li><a href="Biaugmented_pentagonal_prism" title="Biaugmented pentagonal prism">biaugmented pentagonal prism</a></li>

<li><a href="Augmented_hexagonal_prism" title="Augmented hexagonal prism">augmented hexagonal prism</a></li>

<li><a href="Parabiaugmented_hexagonal_prism" title="Parabiaugmented hexagonal prism">parabiaugmented hexagonal prism</a></li>

<li><a href="Metabiaugmented_hexagonal_prism" title="Metabiaugmented hexagonal prism">metabiaugmented hexagonal prism</a></li>

<li><a href="Triaugmented_hexagonal_prism" title="Triaugmented hexagonal prism">triaugmented hexagonal prism</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modified <a href="Platonic_solid" title="Platonic solid">Platonic solids</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Augmented_dodecahedron" title="Augmented dodecahedron">augmented dodecahedron</a></li>

<li><a href="Parabiaugmented_dodecahedron" title="Parabiaugmented dodecahedron">parabiaugmented dodecahedron</a></li>

<li><a href="Metabiaugmented_dodecahedron" title="Metabiaugmented dodecahedron">metabiaugmented dodecahedron</a></li>

<li><a href="Triaugmented_dodecahedron" title="Triaugmented dodecahedron">triaugmented dodecahedron</a></li>

<li><a href="Metabidiminished_icosahedron" title="Metabidiminished icosahedron">metabidiminished icosahedron</a></li>

<li><a href="Tridiminished_icosahedron" title="Tridiminished icosahedron">tridiminished icosahedron</a></li>

<li><a href="Augmented_tridiminished_icosahedron" title="Augmented tridiminished icosahedron">augmented tridiminished icosahedron</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modified <a href="Archimedean_solid" title="Archimedean solid">Archimedean solids</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Augmented_truncated_tetrahedron" title="Augmented truncated tetrahedron">augmented truncated tetrahedron</a></li>

<li><a href="Augmented_truncated_cube" title="Augmented truncated cube">augmented truncated cube</a></li>

<li><a href="Biaugmented_truncated_cube" title="Biaugmented truncated cube">biaugmented truncated cube</a></li>

<li><a href="Augmented_truncated_dodecahedron" title="Augmented truncated dodecahedron">augmented truncated dodecahedron</a></li>

<li><a href="Parabiaugmented_truncated_dodecahedron" title="Parabiaugmented truncated dodecahedron">parabiaugmented truncated dodecahedron</a></li>

<li><a href="Metabiaugmented_truncated_dodecahedron" title="Metabiaugmented truncated dodecahedron">metabiaugmented truncated dodecahedron</a></li>

<li><a href="Triaugmented_truncated_dodecahedron" title="Triaugmented truncated dodecahedron">triaugmented truncated dodecahedron</a></li>

<li><a href="Gyrate_rhombicosidodecahedron" title="Gyrate rhombicosidodecahedron">gyrate rhombicosidodecahedron</a></li>

<li><a href="Parabigyrate_rhombicosidodecahedron" title="Parabigyrate rhombicosidodecahedron">parabigyrate rhombicosidodecahedron</a></li>

<li><a href="Metabigyrate_rhombicosidodecahedron" title="Metabigyrate rhombicosidodecahedron">metabigyrate rhombicosidodecahedron</a></li>

<li><a href="Trigyrate_rhombicosidodecahedron" title="Trigyrate rhombicosidodecahedron">trigyrate rhombicosidodecahedron</a></li>

<li><a href="Diminished_rhombicosidodecahedron" title="Diminished rhombicosidodecahedron">diminished rhombicosidodecahedron</a></li>

<li><a href="Paragyrate_diminished_rhombicosidodecahedron" title="Paragyrate diminished rhombicosidodecahedron">paragyrate diminished rhombicosidodecahedron</a></li>

<li><a href="Metagyrate_diminished_rhombicosidodecahedron" title="Metagyrate diminished rhombicosidodecahedron">metagyrate diminished rhombicosidodecahedron</a></li>

<li><a href="Bigyrate_diminished_rhombicosidodecahedron" title="Bigyrate diminished rhombicosidodecahedron">bigyrate diminished rhombicosidodecahedron</a></li>

<li><a href="Parabidiminished_rhombicosidodecahedron" title="Parabidiminished rhombicosidodecahedron">parabidiminished rhombicosidodecahedron</a></li>

<li><a href="Metabidiminished_rhombicosidodecahedron" title="Metabidiminished rhombicosidodecahedron">metabidiminished rhombicosidodecahedron</a></li>

<li><a href="Gyrate_bidiminished_rhombicosidodecahedron" title="Gyrate bidiminished rhombicosidodecahedron">gyrate bidiminished rhombicosidodecahedron</a></li>

<li><a href="Tridiminished_rhombicosidodecahedron" title="Tridiminished rhombicosidodecahedron">tridiminished rhombicosidodecahedron</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <a href="Elementary_polyhedron" class="mw-redirect" title="Elementary polyhedron">elementary solids</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Snub_disphenoid" title="Snub disphenoid">snub disphenoid</a></li>

<li><a href="Snub_square_antiprism" title="Snub square antiprism">snub square antiprism</a></li>

<li><a href="Sphenocorona" title="Sphenocorona">sphenocorona</a></li>

<li><a href="Augmented_sphenocorona" title="Augmented sphenocorona">augmented sphenocorona</a></li>

<li><a href="Sphenomegacorona" title="Sphenomegacorona">sphenomegacorona</a></li>

<li><a href="Hebesphenomegacorona" title="Hebesphenomegacorona">hebesphenomegacorona</a></li>

<li><a href="Disphenocingulum" title="Disphenocingulum">disphenocingulum</a></li>

<li><a href="Bilunabirotunda" title="Bilunabirotunda">bilunabirotunda</a></li>

<li><a href="Triangular_hebesphenorotunda" title="Triangular hebesphenorotunda">triangular hebesphenorotunda</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>(See also <a href="List_of_Johnson_solids" title="List of Johnson solids">List of Johnson solids</a>, a sortable table)</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 2025-08-08" href="https://en.wikipedia.org/wiki/?title=Augmented_triangular_prism&oldid=1304818180">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.

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