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	Ih, [5,3], (*532) order 120
Rotation group	I, [5,3]^+, (532), order 60
Dual polyhedron	Disdyakis diacositetracontahedron
Properties	convex, zonohedron

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

• Truncated small rhombicosidodecahedron
• Beveled icosidodecahedron

Zonohedron

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

The truncated icosidodecahedron is similar, with all regular faces, and 4.6.10 vertex figure.

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.

Name	Icosidodeca- hedron	Rhomb- icosidodeca- hedron	Truncated rhomb- icosidodeca- hedron	Snub rhomb- icosidodeca- hedron
Coxeter	ID (rD)	rID (rrD)	trID (trrD)	srID (htrrD)
Conway	aD	aaD = eD	taaD = baD	saD
Image
Conway	jD	oD	maD	gaD
Dual

See also

• Expanded icosidodecahedron
• Truncated rhombicuboctahedron

References

1. Eppstein (1996)

• Eppstein, David (1996). "Zonohedra and zonotopes". Mathematica in Education and Research 5 (4): 15–21.
• Coxeter Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 (pp. 145–154 Chapter 8: Truncation)
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5

External links

• George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input