icosidodecahedron
Noun
Meaning
icosidodecahedron (plural icosidodecahedra or icosidodecahedrons)
An Archimedean solid with thirty-two regular faces (twelve pentagons and twenty triangles).
Synonyms
Phrases with the word
Examples
An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon.
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.
In this nomenclature, an octahedron would be a square bipyramid, a cuboctahedron would be a triangular gyrobicupola, and an icosidodecahedron would be a pentagonal gyrobirotunda.
The vertices of the octahedron lie at the midpoints of the edges of the tetrahedron, and in this sense it relates to the tetrahedron in the same way that the cuboctahedron and icosidodecahedron relate to the other Platonic solids.
The icosidodecahedron can therefore be called a pentagonal gyrobirotunda with the gyration between top and bottom halves.
They are precisely the six decagons which form the wire frame figure of the icosidodecahedron.