title: Great dodecicosidodecahedron
text: # Great dodecicosidodecahedron
  
  Great dodecicosidodecahedron :
  
  | Type | Uniform star polyhedron |
  | - | - |
  | Elements | F = 44, E = 120 V = 60 (χ = −16) |
  | Faces by sides | 20{3}+12{5/2}+12{10/3} |
  | Coxeter diagram | |
  | Wythoff symbol | 5/2 3 | 5/3 5/3 3/2 | 5/3 |
  | Symmetry group | $I_h,$ [5,3], *532 |
  | Index references | $U_{61},$ $C_{77},$ $W_{99}$ |
  | Dual polyhedron | Great dodecacronic hexecontahedron |
  | Vertex figure | 3.10/3.5/2.10/7 |
  | Bowers acronym | Gaddid |
  
  In geometry, the great dodecicosidodecahedron (or great dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as $U_{61}.$ It has 44 faces (20 triangles, 12 pentagrams and 12 decagrams), 120 edges and 60 vertices.
  
  ## Related polyhedra
  
  It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the triangular and pentagrammic faces in common), and with the great rhombidodecahedron (having the decagrammic faces in common).
  
  | Nonconvex great rhombicosidodecahedron | Great dodecicosidodecahedron | Great rhombidodecahedron |
  | - | - | - |
  | Truncated great dodecahedron | Compound of six pentagonal prisms | Compound of twelve pentagonal prisms |
  