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Truncated rhombicosidodecahedron

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Truncated rhombicosidodecahedron
Schläfli symbol trr{5,3} =
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 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

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  • Truncated small rhombicosidodecahedron
  • Beveled icosidodecahedron

Zonohedron

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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]

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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

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References

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  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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