Truncated tetrakis cube
# 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 |
| - | - |
