title: Truncated tetrakis cube
text: # Truncated tetrakis cube
  
  Truncated tetrakis cube Hexatruncated tetrakis cube :
  
  | Conway notation | t6kC = dk6tO |
  | - | - |
  | Faces | 8 hexagons 24 pentagons |
  | Edges | 84 |
  | Vertices | 54 |
  | Dual | Hexakis truncated octahedron |
  | Vertex configuration | 6 (5.5.5.5) 48 (5.5.6) |
  | Symmetry group | $O_h$ |
  | Properties | convex |
  
  The truncated tetrakis cube, or more precisely an order-6 truncated tetrakis cube or hexatruncated tetrakis cube, is a convex polyhedron with 32 faces: 24 sets of 3 bilateral symmetry pentagons arranged in an octahedral arrangement, with 8 regular hexagons in the gaps.
  
  ## Construction
  
  It is constructed from taking a tetrakis cube by truncating the order-6 vertices. This creates 4 regular hexagon faces, and leaves 12 mirror-symmetric pentagons.
  
  * tetrakis cube
  
  ## Hexakis truncated octahedron
  
  The dual of the order-6 truncated triakis tetrahedron is called a hexakis truncated octahedron. It is constructed by a truncated octahedron with hexagonal pyramids augmented.
  
  | Truncated octahedron | hexakis truncated octahedron |
  | - | - |
  