Truncated triakis tetrahedron

Not to be confused with triakis truncated tetrahedron.

Truncated triakis tetrahedron
Conway notation	t6kT
Faces	4 hexagons 12 pentagons
Edges	42
Vertices	28
Dual	Hexakis truncated tetrahedron
Vertex configuration	4 (5.5.5) 24 (5.5.6)
Symmetry group	Td
Properties	convex

The truncated triakis tetrahedron is a convex polyhedron with 16 faces: 4 sets of 3 pentagons arranged in a tetrahedral arrangement, with 4 hexagons in the gaps. It is constructed from taking a triakis tetrahedron by truncating the order-6 vertices. This creates 4 regular hexagon faces, and leaves 12 irregular pentagons.

A topologically similar equilateral polyhedron can be constructed by using 12 regular pentagons with 4 equilateral but nonplanar hexagons, each vertex with internal angles alternating between 108 and 132 degrees.

Full truncation

If all of a triakis tetrahedron's vertices, of both kinds, are truncated, the resulting solid is an irregular icosahedron, whose dual is a trihexakis truncated tetrahedron.

Truncation of only the simpler vertices yields what looks like a tetrahedron with each face raised by a low triangular frustum. The dual to that truncation will be the triakis truncated tetrahedron.

The full truncation

See also

• Near-miss Johnson solid

External links

• Johnson Solid Near Misses: Number 22
• George Hart's Polyhedron generator - "t6kT" (Conway polyhedron notation)