Editing Icosidodecahedron (section)

=== Related polyhedra ===
[[File:Icosidecahedron in truncated cube.png|120px|thumb|A topological icosi&shy;dodeca&shy;hedron in truncated cube, inserting 6 vertices in center of octagons, and dissecting them into 2 pentagons and 2 triangles.]]
The [[truncated cube]] can be turned into an icosidodecahedron by dividing the octagons into two pentagons and two triangles. It has [[pyritohedral symmetry]].

Eight [[uniform star polyhedron|uniform star polyhedra]] share the same [[vertex arrangement]]. Of these, two also share the same [[edge arrangement]]: the [[small icosihemidodecahedron]] (having the triangular faces in common), and the [[small dodecahemidodecahedron]] (having the pentagonal faces in common). The vertex arrangement is also shared with the [[uniform polyhedron compound|compounds]] of [[compound of five octahedra|five octahedra]] and of [[compound of five tetrahemihexahedra|five tetrahemihexahedra]].
{|class="wikitable" width="400" style="vertical-align:top;text-align:center"
|align=center|[[Image:Icosidodecahedron.png|100px]]<br>Icosidodecahedron
|align=center|[[Image:Small icosihemidodecahedron.png|100px]]<br>[[Small icosihemidodecahedron]]
|align=center|[[Image:Small dodecahemidodecahedron.png|100px]]<br>[[Small dodecahemidodecahedron]]
|-
|align=center|[[Image:Great icosidodecahedron.png|100px]]<br>[[Great icosidodecahedron]]
|align=center|[[Image:Great dodecahemidodecahedron.png|100px]]<br>[[Great dodecahemidodecahedron]]
|align=center|[[Image:Great icosihemidodecahedron.png|100px]]<br>[[Great icosihemidodecahedron]]
|-
|align=center|[[Image:Dodecadodecahedron.png|100px]]<br>[[Dodecadodecahedron]]
|align=center|[[Image:Small dodecahemicosahedron.png|100px]]<br>[[Small dodecahemicosahedron]]
|align=center|[[Image:Great dodecahemicosahedron.png|100px]]<br>[[Great dodecahemicosahedron]]
|-
|align=center|[[Image:Compound of five octahedra.png|100px]]<br>[[Compound of five octahedra]]
|align=center|[[Image:UC18-5 tetrahemihexahedron.png|100px]]<br>[[Compound of five tetrahemihexahedra]]
|}