Truncated rhombicosidodecahedronSchläfli symboltrr{5,3} = Conway notationtaD = baDFaces122:60 {4}20 {6}30 {8}12 {10}Edges360Vertices240Symmetry groupIh, [5,3], (*532) order 120Rotation groupI, [5,3]+, (532), order 60Dual polyhedronDisdyakis hexecontahedronPropertiesconvex 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.Eppstein (1996)
Related polyhedra The truncated icosidodecahedron is similar, with all regular faces, and 4.6.10 vertex figure. Also see the truncated rhombirhombicosidodecahedron.
truncated icosidodecahedronTruncated rhombicosidodecahedron4.6.104.8.10 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. NameIcosidodeca-hedronRhomb-icosidodeca-hedronTruncated rhomb-icosidodeca-hedronSnub rhomb-icosidodeca-hedronCoxeterID (rD)rID (rrD)trID (trrD)srID (htrrD)ConwayaDaaD = eDtaaD = baDsaDImageConwayjDoDmaDgaDDual
See also Expanded icosidodecahedron Truncated rhombicuboctahedron
References
Coxeter Regular Polytopes, Third edition, (1973), Dover edition, (pp. 145–154 Chapter 8: Truncation) John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008,
External links George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input