Icosidodecahedron
In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces. 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. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.
| Icosidodecahedron | |
|---|---|
(Click here for rotating model) | |
| Type | Archimedean solid Uniform polyhedron |
| Elements | F = 32, E = 60, V = 30 (χ = 2) |
| Faces by sides | 20{3}+12{5} |
| Conway notation | aD |
| Schläfli symbols | r{5,3} |
| t1{5,3} | |
| Wythoff symbol | 2 | 3 5 |
| Coxeter diagram | |
| Symmetry group | Ih, H3, [5,3], (*532), order 120 |
| Rotation group | I, [5,3]+, (532), order 60 |
| Dihedral angle | |
| References | U24, C28, W12 |
| Properties | Semiregular convex quasiregular |
Colored faces |
3.5.3.5 (Vertex figure) |
Rhombic triacontahedron (dual polyhedron) |
Net |
![{\displaystyle {\begin{aligned}&\cos ^{-1}\left(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\\[2pt]&\approx 142.62^{\circ }\end{aligned}}}](../I/09e79aad1401f46d84102bb477c0240111bc8c4f.svg)
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