Truncated rhombicosidodecahedron

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Truncated rhombicosidodecahedron
Truncated small rhombicosidodecahedron.png
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
Disdyakis dihectatetracontahedron.png
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[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.

Uniform polyhedron-53-t012.png
4.6.10
Truncated rhombicosidodecahedron2.png
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 Uniform polyhedron-53-t1.png Uniform polyhedron-53-t02.png Truncated rhombicosidodecahedron2.png Snub rhombicosidodecahedron2.png
Conway jD oD maD gaD
Dual Rhombictriacontahedron.svg Deltoidalhexecontahedron.jpg Disdyakis dihectatetracontahedron.png Pentagonal hecatonicosahedron.png

See also[edit]

References[edit]

  1. ^ Eppstein (1996)

External links[edit]