Type Uniform star polyhedron
Elements F = 44, E = 180
V = 120 (χ = −16)
Faces by sides 20{6}+12{10}+12{10/3}
Coxeter diagram
Wythoff symbol 3 5 5/3 |
Symmetry group Ih, [5,3], *532
Index references U45, C57, W84
Dual polyhedron Tridyakis icosahedron
Vertex figure
6.10.10/3
Bowers acronym Idtid

In

nonconvex uniform polyhedron
, indexed as U45.

## Convex hull

Its convex hull is a nonuniform truncated icosidodecahedron.

 Truncated icosidodecahedron Convex hull Icositruncated dodecadodecahedron

## Cartesian coordinates

Cartesian coordinates
for the vertices of an icositruncated dodecadodecahedron are all the even permutations of ${\displaystyle {\begin{array}{crrlc}{\Bigl (}&\pm {\bigl [}2-{\frac {1}{\varphi }}{\bigr ]},&\pm \,1,&\pm {\bigl [}2+\varphi {\bigr ]}&{\Bigr )},\\{\Bigl (}&\pm \,1,&\pm \,{\frac {1}{\varphi ^{2}}},&\pm {\bigl [}3\varphi -1{\bigr ]}&{\Bigr )},\\{\Bigl (}&\pm \,2,&\pm \,{\frac {2}{\varphi }},&\pm \,2\varphi &{\Bigr )},\\{\Bigl (}&\pm \,3,&\pm \,{\frac {1}{\varphi ^{2}}},&\pm \,\varphi ^{2}&{\Bigr )},\\{\Bigl (}&\pm \,\varphi ^{2},&\pm \,1,&\pm {\bigl [}3\varphi -2{\bigr ]}&{\Bigr )},\end{array}}}$

where ${\displaystyle \varphi ={\tfrac {1+{\sqrt {5}}}{2}}}$ is the golden ratio.

### Tridyakis icosahedron

Tridyakis icosahedron
Type Star polyhedron
Face
Elements F = 120, E = 180
V = 44 (χ = −16)
Symmetry group Ih, [5,3], *532
Index references DU45