Simplicial polytope

<h2 id="examples">Examples</h2>
<p>Simplicial <a href="/facts/Polyhedra/UC0p9FTF">polyhedra</a> include:
</p>
<ul><li><a href="/facts/Bipyramid/MkzrCA0W">Bipyramids</a></li>
<li><a href="/facts/Gyroelongated_bipyramid/g8Kln53f">Gyroelongated bipyramids</a></li>
<li><a href="/facts/Deltahedron/qDjkasx9">Deltahedra</a> (equilateral triangles)
<ul><li><a href="/facts/Platonic_solid/jraREXFD">Platonic</a>
<ul><li><a href="/facts/Tetrahedron/7mkSrl6j">tetrahedron</a>, <a href="/facts/Octahedron/G38q92xW">octahedron</a>, <a href="/facts/Icosahedron/wWbpnDYp">icosahedron</a></li></ul></li>
<li><a href="/facts/Johnson_solid/8SR7CyNz">Johnson solids</a>:
<ul><li><a href="/facts/Triangular_bipyramid/fU4kIBTV">triangular bipyramid</a>, <a href="/facts/Pentagonal_bipyramid/Mt3bUSPI">pentagonal bipyramid</a>, <a href="/facts/Snub_disphenoid/kdLUzB07">snub disphenoid</a>, <a href="/facts/Triaugmented_triangular_prism/SAFVrVey">triaugmented triangular prism</a>, <a href="/facts/Gyroelongated_square_dipyramid/fIP8gBx4">gyroelongated square dipyramid</a></li></ul></li></ul></li>
<li><a href="/facts/Catalan_solid/R8D2cP7D">Catalan solids</a>:
<ul><li><a href="/facts/Triakis_tetrahedron/qz6NNDMU">triakis tetrahedron</a>, <a href="/facts/Triakis_octahedron/mJ3s18DL">triakis octahedron</a>, <a href="/facts/Tetrakis_hexahedron/RjfM6K49">tetrakis hexahedron</a>, <a href="/facts/Disdyakis_dodecahedron/wwAbxHWL">disdyakis dodecahedron</a>, <a href="/facts/Triakis_icosahedron/VoVKELcj">triakis icosahedron</a>, <a href="/facts/Pentakis_dodecahedron/TksT30Qt">pentakis dodecahedron</a>, <a href="/facts/Disdyakis_triacontahedron/WkV7L9Pg">disdyakis triacontahedron</a></li></ul></li></ul>
<p>Simplicial tilings:
</p>
<ul><li>Regular:
<ul><li><a href="/facts/Triangular_tiling/Jx8f8Krh">triangular tiling</a></li></ul></li>
<li><a href="/facts/Laves_tiling/c1ALUDMm">Laves tilings</a>:
<ul><li><a href="/facts/Tetrakis_square_tiling/oqpMEMBw">tetrakis square tiling</a>,  <a href="/facts/Triakis_triangular_tiling/c9dRoGFS">triakis triangular tiling</a>, <a href="/facts/Kisrhombille_tiling/qMT9oGKC">kisrhombille tiling</a></li></ul></li></ul>
<p>Simplicial <a href="/facts/4-polytope/mY8vBpec">4-polytopes</a> include:
</p>
<ul><li><a href="/facts/Convex_regular_4-polytope/lFf8IH1C">convex regular 4-polytope</a>
<ul><li><a href="/facts/Pentachoron/Rh6lwDcc">4-simplex</a>, <a href="/facts/16-cell/X0YAfobw">16-cell</a>, <a href="/facts/600-cell/tNBtDUe9">600-cell</a></li></ul></li>
<li>Dual <a href="/facts/Convex_uniform_honeycomb/78IkTl7A">convex uniform honeycombs</a>:
<ul><li><a href="/facts/Disphenoid_tetrahedral_honeycomb/Ae30mwnf">Disphenoid tetrahedral honeycomb</a></li>
<li>Dual of <a href="/facts/Cantitruncated_cubic_honeycomb/eMxySFur">cantitruncated cubic honeycomb</a></li>
<li>Dual of <a href="/facts/Omnitruncated_cubic_honeycomb/eMxySFur">omnitruncated cubic honeycomb</a></li>
<li>Dual of <a href="/facts/Cantitruncated_alternated_cubic_honeycomb/mX4CxSvp">cantitruncated alternated cubic honeycomb</a></li></ul></li></ul>
<p>Simplicial higher polytope families:
</p>
<ul><li><a href="/facts/Simplex/0FCfNRN8">simplex</a></li>
<li><a href="/facts/Cross-polytope/erk0byF6">cross-polytope</a> (Orthoplex)</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Simplicial_complex/fF2282CF">Simplicial complex</a></li>
<li><a href="/facts/Delaunay_triangulation/6VRk7cS9">Delaunay triangulation</a></li></ul>
<h2 id="notes">Notes</h2>

<ul><li>Cromwell, Peter R. (1997). <a href="https://books.google.com/books?id=OJowej1QWpoC&q=Polyhedra&pg=PP1"><i>Polyhedra</i></a>. Cambridge University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-521-66405-5.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Polyhedra, Peter R. Cromwell, 1997. (p.341) <a href="https://books.google.com/books?id=OJowej1QWpoC" target="_blank">https://books.google.com/books?id=OJowej1QWpoC</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Simplicial polytope open-in-new

Simplicial polytope