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
pentagon
In geometry, a pentagon (from the Greek language, Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is ...
s arranged in an
octahedral
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
arrangement, with 8 regular
hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Regular hexagon
A ''regular hexagon'' h ...
s 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.
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
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagons and 6 squares), 36 ...
with
hexagonal pyramid
In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point (the apex). Like any pyramid, it is self- dual.
A right hexagonal pyramid with a regular hexagon base ...
s augmented.
See also
*
Truncated triakis tetrahedron
In geometry, the truncated triakis tetrahedron, or more precisely an order-6 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.
Const ...
*
Truncated triakis octahedron
The truncated triakis octahedron, or more precisely an order-8 truncated triakis octahedron, is a convex polyhedron with 30 faces: 8 sets of 3 pentagons arranged in an octahedral arrangement, with 6 octagons in the gaps.
Triakis octahedron
It is ...
*
Truncated triakis icosahedron
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 icosahedro ...
External links
George Hart's Polyhedron generator- "t6kC" (
Conway polyhedron notation
In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations.
Conway and Hart extended the idea of using o ...
)
Polyhedra
{{Polyhedron-stub