Editing Icosidodecahedron (section)

=== Related polychora ===

In four-dimensional geometry, the icosidodecahedron appears in the [[Regular polytopes|regular]] [[600-cell]] as the equatorial slice that belongs to the vertex-first passage of the 600-cell through 3D space. In other words: the 30 vertices of the 600-cell which lie at arc distances of 90 degrees on its circumscribed [[hypersphere]] from a pair of opposite vertices, are the vertices of an icosidodecahedron. The wireframe figure of the 600-cell consists of 72 flat regular decagons. Six of these are the equatorial decagons to a pair of opposite vertices, and these six form the wireframe figure of an icosidodecahedron.

If a [[600-cell]] is [[Stereographic projection|stereographically projected]] to 3-space about any vertex and all points are normalised, the [[geodesic]]s upon which edges fall comprise the icosidodecahedron's [[Barycentric subdivision#Barycentric subdivision of a convex polytope|barycentric subdivision]].