Truncated dodecahedron  

(Click here for rotating model) 

Type  Archimedean solid 
Elements  F = 32, E = 90, V = 60 (χ = 2) 
Faces by sides  20{3}+12{10} 
Schläfli symbol  t{5,3} 
Wythoff symbol  2 3  5 
CoxeterDynkin  
Symmetry  I_{h} or (*532) 
References  U_{26}, C_{29}, W_{10} 
Properties  Semiregular convex 
Colored faces 
3.10.10 (Vertex figure) 
Triakis icosahedron (dual polyhedron) 
Net 
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.
Contents 
This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles.
It is part of a truncation process between a dodecahedron and icosahedron:
Dodecahedron 
Truncated dodecahedron 
Icosidodecahedron 
Truncated icosahedron 
Icosahedron 
It shares its vertex arrangement with three nonconvex uniform polyhedra:
Truncated dodecahedron 
Great icosicosidodecahedron 
Great ditrigonal dodecicosidodecahedron 
Great dodecicosahedron 
It is used in the celltransitive hyperbolic spacefilling tessellation, the bitruncated icosahedral honeycomb.
The area A and the volume V of a truncated dodecahedron of edge length a are:
The following Cartesian coordinates define the vertices of a truncated dodecahedron with edge length 2(τ1), centered at the origin:
where τ = (1+√5)/2 is the golden ratio (also written φ).

