Truncated hexagonal trapezohedron

The truncated hexagonal trapezohedron is the fourth in an infinite series of truncated trapezohedron polyhedra. It has 12 pentagon and 2 hexagon faces.

Truncated hexagonal trapezohedron
TypeTruncated trapezohedron
Conwayt6dA6
Faces12 pentagons, 2 hexagons
Edges36
Vertices24
Symmetry groupD6d, [12,2+], 2*6, order 24
Rotation groupD6, [6,2]+, 226, order 12
Dual polyhedronGyroelongated hexagonal dipyramid
Propertiesconvex

This polyhedron can be constructed by taking a hexagonal trapezohedron and truncating the polar axis vertices.

Weaire–Phelan structure

Another form of this polyhedron has D2d symmetry and is a part of a space-filling honeycomb along with an irregular dodecahedron, called Weaire–Phelan structure.


irregular tetradecahedron
(Truncated hexagonal trapezohedron)

Weaire–Phelan honeycomb
gollark: Well, they've closed schools and are cancelling GCSEs.
gollark: Ah, I see.
gollark: Explain what?
gollark: Not Doc®, a-dork-able.
gollark: Some offense, but this may be why people dislike you.

See also

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