Editing Hexagon (section)

===Polyhedra with hexagons===
There is no [[Platonic solid]] made of only regular hexagons, because the hexagons [[tessellation|tessellate]], not allowing the result to "fold up". The [[Archimedean solid]]s with some hexagonal faces are the [[truncated tetrahedron]], [[truncated octahedron]], [[truncated icosahedron]] (of [[soccer ball]] and [[fullerene]] fame), [[truncated cuboctahedron]] and the [[truncated icosidodecahedron]]. These hexagons can be considered [[truncation (geometry)|truncated]] triangles, with [[Coxeter diagram]]s of the form {{CDD|node_1|3|node_1|p|node}} and {{CDD|node_1|3|node_1|p|node_1}}.

{| class="wikitable collapsible collapsed" style="text-align:center;"
!colspan=12|Hexagons in [[Archimedean solid]]s
|-
! [[Tetrahedral symmetry|Tetrahedral]]
!colspan=2| [[Octahedral symmetry|Octahedral]]
!colspan=2| [[Icosahedral symmetry|Icosahedral]]
|-
| {{CDD|node_1|3|node_1|3|node}}
| {{CDD|node_1|3|node_1|4|node}}
| {{CDD|node_1|3|node_1|4|node_1}}
| {{CDD|node_1|3|node_1|5|node}}
| {{CDD|node_1|3|node_1|5|node_1}}
|- valign=top
| [[File:truncated tetrahedron.png|100px]]<br>[[truncated tetrahedron]]
| [[File:truncated octahedron.png|100px]]<br>[[truncated octahedron]]
| [[File:Great rhombicuboctahedron.png|100px]]<br>[[truncated cuboctahedron]]
| [[File:truncated icosahedron.png|100px]]<br>[[truncated icosahedron]]
| [[File:Great rhombicosidodecahedron.png|100px]]<br>[[truncated icosidodecahedron]]
|}

There are other symmetry polyhedra with stretched or flattened hexagons, like these [[Goldberg polyhedron]] G(2,0):
{| class="wikitable collapsible collapsed" style="text-align:center;"
! colspan=12 | Hexagons in Goldberg polyhedra
|-
! [[Tetrahedral symmetry|Tetrahedral]]
! [[Octahedral symmetry|Octahedral]]
! [[Icosahedral symmetry|Icosahedral]]
|-
| [[File:Alternate truncated cube.png|120px]]<BR>[[Chamfered tetrahedron]]
| [[File:Truncated rhombic dodecahedron2.png|120px]]<BR>[[Chamfered cube]]
| [[File:Truncated rhombic triacontahedron.png|120px]]<BR>[[Chamfered dodecahedron]]
|}

There are also 9 [[Johnson solid]]s with regular hexagons:
{| class="wikitable collapsible collapsed" style="width:400px; text-align:center;"
!colspan=12| Johnson solids with hexagons
|- valign=top
| [[File:Triangular cupola.png|80px]]<BR>[[triangular cupola]]
| [[File:Elongated triangular cupola.png|80px]]<BR>[[elongated triangular cupola]]
| [[File:Gyroelongated triangular cupola.png|80px]]<BR>[[gyroelongated triangular cupola]]
|- valign=top
| [[File:Augmented hexagonal prism.png|80px]]<BR>[[augmented hexagonal prism]]
| [[File:Parabiaugmented hexagonal prism.png|80px]]<BR>[[parabiaugmented hexagonal prism]]
| [[File:Metabiaugmented hexagonal prism.png|80px]]<BR>[[metabiaugmented hexagonal prism]]
|- valign=top
| [[File:Triaugmented hexagonal prism.png|80px]]<BR>[[triaugmented hexagonal prism]]
| [[File:Augmented truncated tetrahedron.png|80px]]<BR>[[augmented truncated tetrahedron]]
| [[File:Triangular hebesphenorotunda.png|80px]]<BR>[[triangular hebesphenorotunda]]
|}

{| class="wikitable collapsible collapsed" style="text-align:center;"
!colspan=12| [[Prismoid]]s with hexagons
|- valign=top
| [[File:Hexagonal prism.png|100px]]<br>[[Hexagonal prism]]
| [[File:Hexagonal antiprism.png|100px]]<br>[[Hexagonal antiprism]]
| [[File:Hexagonal pyramid.png|100px]]<br>[[Hexagonal pyramid]]
|}

{| class="wikitable collapsible collapsed" style="width:480px;"
!colspan=12| Tilings with regular hexagons
|-
! Regular
!colspan=3| 1-uniform
|- style="text-align:center;"
|[[hexagonal tiling|{6,3}]]<BR>{{CDD|node_1|6|node|3|node}}
|[[Trihexagonal tiling|r{6,3}]]<BR>{{CDD|node|6|node_1|3|node}}
|[[Rhombitrihexagonal tiling|rr{6,3}]]<BR>{{CDD|node_1|6|node|3|node_1}}
|[[Truncated trihexagonal tiling|tr{6,3}]]<BR>{{CDD|node_1|6|node_1|3|node_1}}
|-
|[[Image:Uniform tiling 63-t0.svg|120px]]
|[[Image:Uniform tiling 63-t1.png|120px]]
|[[Image:Uniform polyhedron-63-t02.png|120px]]
|[[Image:Uniform polyhedron-63-t012.png|120px]]
|- style="text-align:center;"
|colspan=4|[[2-uniform tiling]]s
|-
|[[File:2-uniform 1.png|120px]]
|[[File:2-uniform 10.png|120px]]
|[[File:2-uniform 11.png|120px]]
|[[File:2-uniform 12.png|120px]]
|}