Truncated tetrakis cube

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.

Truncated tetrakis cube
Hexatruncated tetrakis cube
Conway notationt6kC = dk6tO
Faces8 hexagons
24 pentagons
Edges84
Vertices54
DualHexakis truncated octahedron
Vertex configuration6 (5.5.5.5)
48 (5.5.6)
Symmetry groupOh
Propertiesconvex

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

See also


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