title: Truncated triakis icosahedron
text: # Truncated triakis icosahedron
  
  Truncated triakis icosahedron :
  
  | Conway notation | t10kI = dk10tD |
  | - | - |
  | Faces | 12 decagons 60 pentagons |
  | Edges | 210 |
  | Vertices | 140 |
  | Dual | Decakis truncated dodecahedron |
  | Vertex configuration | 12 (5.5.5) 60 (5.5.10) |
  | Symmetry group | $I_h$ |
  | Properties | convex |
  | Net ||
  
  The truncated triakis icosahedron, or more precisely an order-10 truncated triakis icosahedron, is a convex polyhedron with 72 faces: 10 sets of 3 pentagons arranged in an icosahedral arrangement, with 12 decagons in the gaps.
  
  ## Triakis icosahedron
  
  It is constructed from taking a triakis icosahedron by truncating the order-10 vertices. This creates 12 regular decagon faces, and leaves 60 mirror-symmetric pentagons.
  
  * Triakis icosahedron
  
  ## Decakis truncated dodecahedron
  
  The dual of the truncated triakis icosahedron is called a decakis truncated dodecahedron. It can be seen as a truncated dodecahedron with decagonal pyramids augmented to the faces.
  
  | Truncated dodecahedron | Decakis truncated dodecahedron | Net |
  | - | - | - |
  