title: Truncated rhombicosidodecahedron
text: # 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 | $I_h,$ [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
  
  * 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.
  
  ## Related polyhedra
  
  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 | | | | |
  