Editing Regular polyhedron (section)

== The regular polyhedra ==

There are five [[Convex polygon|convex]] regular polyhedra, known as the '''[[Platonic solid]]s'''; four regular [[star polyhedron|star polyhedra]], the '''[[Kepler–Poinsot polyhedra]]'''; and five regular compounds of regular polyhedra:

=== Platonic solids ===
{{Main|Platonic solid}}

{| class="wikitable" width=640
|- align=center
|[[Image:Tetrahedron.jpg|100px]]
|[[Image:Hexahedron.jpg|100px]]
|[[Image:Octahedron.jpg|100px]]
|[[Image:Dodecahedron.jpg|100px]]
|[[Image:Icosahedron.jpg|100px]]
|- align=center
|[[Tetrahedron]]<br>{3,&nbsp;3}||[[Cube]]<br>{4,&nbsp;3}||[[Octahedron]]<br>{3,&nbsp;4}||[[Regular dodecahedron|Dodecahedron]]<br>{5,&nbsp;3}||[[Regular icosahedron|Icosahedron]]<br>{3,&nbsp;5}
|- align=center
|[[Euler characteristic|''χ'']] = 2||''χ'' = 2||''χ'' = 2||''χ'' = 2||''χ'' = 2
|}

=== Kepler–Poinsot polyhedra ===

{{Main|Kepler–Poinsot polyhedra}}

{| class="wikitable" width=640
|- align=center
|[[Image:SmallStellatedDodecahedron.jpg|100px]]
|[[Image:GreatDodecahedron.jpg|100px]]
|[[Image:GreatStellatedDodecahedron.jpg|100px]]
|[[Image:GreatIcosahedron.jpg|100px]]
|- align=center
|[[Small stellated dodecahedron]]<br>{5/2,&nbsp;5}
||[[Great dodecahedron]]<br>{5,&nbsp;5/2}
||[[Great stellated dodecahedron]]<br>{5/2,&nbsp;3}
||[[Great icosahedron]]<br>{3,&nbsp;5/2}
|- align=center
|''χ'' = −6||''χ'' = −6||''χ'' = 2||''χ'' = 2
|}

=== Regular compounds ===
{{Main|Polytope compound#Regular compounds}}

{| class="wikitable" style="width:640px; text-align:center;"
|-
| [[Image:Compound of two tetrahedra.png|100px]]
| [[Image:Compound of five tetrahedra.png|100px]]
| [[Image:Compound of ten tetrahedra.png|100px]]
| [[Image:Compound of five cubes.png|100px]]
| [[Image:Compound of five octahedra.png|100px]]
|-
| [[Stellated octahedron|Two tetrahedra]]<br>2 {3,&nbsp;3}
| [[Compound of five tetrahedra|Five tetrahedra]]<br>5 {3,&nbsp;3}
| [[Compound of ten tetrahedra|Ten tetrahedra]]<br>10 {3,&nbsp;3}
| [[Compound of five cubes|Five cubes]]<br>5 {4,&nbsp;3}
| [[Compound of five octahedra|Five octahedra]]<br>5 {3,&nbsp;4}
|-
| ''χ'' = 4 || ''χ'' = 10 || ''χ'' = 0 || ''χ'' = −10 || ''χ'' = 10
|}