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==General tilings== ...4=Ziff |first4=Robert M. |date=2024 |title=Entropy and chirality in sphinx tilings |url=https://link.aps.org/doi/10.1103/PhysRevResearch.6.013227 |journal=Phy ...

[[Triangular prism]] [[File:Triangular prism.png|20px]] |bgcolor=#e7dcc3|[[Vertex figure]]||[[triangular prism]]-based tilted pyramid ...

...e]] [[File:Truncated hexahedron.png|20px]] <BR>[[Triangular prism]] [[File:Triangular prism.png|20px]]<BR>[[Octagonal prism]] [[File:Octagonal prism.png|20px]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

!bgcolor=#e7dcc3 colspan=2|Triangular tiling honeycomb |bgcolor=#e7dcc3|Cells||[[Triangular tiling|{3,6}]] [[File:Uniform tiling 63-t2.svg|40px]] [[File:Uniform tiling ...

...]]<BR>[[Cube]] [[File:Hexahedron.png|20px]]<BR>[[Triangular prism]] [[File:Triangular prism.png|20px]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

...n]] [[File:Truncated tetrahedron.png|20px]]<BR>[[Triangular prism]] [[File:Triangular prism.png|20px]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

|bgcolor=#e7dcc3|[[Vertex figure]]||[[triangular tiling|{3,6}]] or {3^[3]}<BR>[[File:Uniform tiling 63-t2.svg|40px ...of this honeycomb is a triangular tiling. Thus, infinitely many hexagonal tilings meet at each vertex of this honeycomb.<ref>Coxeter ''The Beauty of Geometry ...

...ls|||[[tetrahedron|{3,3}]] [[File:Uniform polyhedron-33-t0.png|40px]]<br>[[triangular tiling|{3^[3]}]] [[Image:Uniform tiling 333-t0.png|40px]] ...semiregular polytope|semiregular]] tessellation with [[tetrahedron]] and [[triangular tiling]] cells arranged in an [[octahedron]] [[vertex figure]]. It is named ...

...[[Octahedron]] [[File:Octahedron.png|20px]]<BR>[[Triangular prism]] [[File:Triangular prism.png|20px]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

...]]<BR>[[Cube]] [[File:Hexahedron.png|20px]]<BR>[[Triangular prism]] [[File:Triangular prism.png|20px]] |bgcolor=#e7dcc3|[[Vertex figure]]||triangular-antipodial antifastigium ...

...[vertex figure]] of this honeycomb is a tetrahedron. Thus, four hexagonal tilings meet at each vertex of this honeycomb, six hexagons meet at each vertex, an ...splitcross|branch_11}}, representing different types (colors) of hexagonal tilings in the [[Wythoff construction]]. ...

...[[File:Small rhombicuboctahedron.png|20px]]<BR>[[Triangular prism]] [[File:Triangular prism.png|20px]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

..., it has three [[square tiling]]s, {4,4}, around each edge, and six square tilings around each vertex, in a [[cube|cubic]] {4,3} [[vertex figure]].<ref>Coxete ...}, and lastly a construction with three types (colors) of checkered square tilings {{CDD|node_1|4|node|4|node_g|3sg|node_g}} ↔ {{CDD|node|4|node_1|split1-44|n ...

...vertex figure]] of this honeycomb is an octahedron. Thus, eight hexagonal tilings meet at each vertex of this honeycomb, and the six edges meeting at each ve ...A quarter-symmetry construction also exists, with four colors of hexagonal tilings: {{CDD|label6|branch_10r|3ab|branch_10l|label6}}. ...

...[[vertex figure]] of this honeycomb is an icosahedron. Thus, 20 hexagonal tilings meet at each vertex of this honeycomb.<ref>Coxeter ''The Beauty of Geometry ..._10ru|split2|node|5|node}}, with [[regular icosahedron|icosahedron]] and [[triangular tiling]] cells. ...

|bgcolor=#e7dcc3|Cell type||[[cube|{4,3}]]<BR>[[Tetrahedron|{3,3}]]<BR>[[Triangular prism|{3}×{}]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

...ed cube|t{4,3}]]<BR>[[tetrahedron|{3,3}]]<BR>[[cuboctahedron|r{4,3}]]<BR>[[triangular prism|{3}×{}]]<BR>[[octagonal prism|t{4}×{}]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

...]]<BR>[[truncated tetrahedron|t{3,3}]]<BR>[[hexagonal prism|t{3}×{}]]<BR>[[triangular prism|{3}×{}]] ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

..._polyhedron|subdivided icosahedron]]''' is a [[convex polyhedron]] with 80 triangular [[Face (geometry)|faces]], 120 [[Edge (geometry)|edges]], and 42 [[Vertex ( ...also be topologically constructed from the [[icosahedron]], dividing each triangular face into 4 triangles by adding mid-edge vertices. If this is all that is d ...

![[Triangular tiling]] In [[2 dimensions]], the honeycomb represents the [[triangular tiling]], with Coxeter graph {{CDD|node_1|split1|branch}} filling the plane ...