Truncated rhombicosidodecahedron

Truncated rhombicosidodecahedron

Schläfli symbol	trr{5,3} = $tr{\begin{Bmatrix}5\\3\end{Bmatrix}}$
Conway notation	taD = baD
Faces	122: 60 {4} 20 {6} 30 {8} 12 {10}
Edges	360
Vertices	240
Symmetry group	I_h, [5,3], (*532) order 120
Rotation group	I, [5,3]⁺, (532), order 60
Dual polyhedron	Disdyakis hexecontahedron
Properties	convex

In geometry, the truncated rhombicosidodecahedron is a polyhedron, constructed as a truncated rhombicosidodecahedron. It has 122 faces: 12 decagons, 30 octagons, 20 hexagons, and 60 squares.

Other names[edit]

Truncated small rhombicosidodecahedron
Beveled icosidodecahedron

Zonohedron[edit]

As a zonohedron, it can be constructed with all but 30 octagons as regular polygons. It is 2-uniform, with 2 sets of 120 vertices existing on two distances from its center.

This polyhedron represents the Minkowski sum of a truncated icosidodecahedron, and a rhombic triacontahedron.^[1]

Related polyhedra[edit]

The truncated icosidodecahedron is similar, with all regular faces, and 4.6.10 vertex figure. Also see the truncated rhombirhombicosidodecahedron.

truncated icosidodecahedron	Truncated rhombicosidodecahedron
4.6.10	4.8.10 and 4.6.8

The truncated rhombicosidodecahedron can be seen in sequence of rectification and truncation operations from the icosidodecahedron. A further alternation step leads to the snub rhombicosidodecahedron.