Truncated rhombicosidodecahedron

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.

Truncated rhombicosidodecahedron
Schläfli symboltrr{5,3} =
Conway notationtaD = baD
Faces122:
60 {4}
20 {6}
30 {8}
12 {10}
Edges360
Vertices240
Symmetry groupIh, [5,3], (*532) order 120
Rotation groupI, [5,3]+, (532), order 60
Dual polyhedronDisdyakis hexecontahedron
Propertiesconvex

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]

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.

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

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
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