Hexagonal-truncated tetrahedral duoprism

Hexagonal-truncated tetrahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Hatut
Coxeter diagram	x6o x3x3o ()
Elements
Tera	4 triangular-hexagonal duoprisms, 4 hexagonal duoprisms, 6 truncated tetrahedral prisms
Cells	24 triangular prisms, 6+12+24 hexagonal prisms, 6 truncated tetrahedra
Faces	24 triangles, 36+72 squares, 12+24 hexagons
Edges	36+72+72
Vertices	72
Vertex figure	Digonal disphenoidal pyramid, edge lengths 1, √3, √3 (base triangle), √3 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {38}}{4}}\approx 1.54110$
Hypervolume	${\frac {23{\sqrt {6}}}{8}}\approx 7.04228$
Diteral angles	Tuttip–tut–tuttip: 120°
	Thiddip-hip-hiddip: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	Thiddip–trip–tuttip: 90°
	Hiddip-hip-tuttip: 90°
	Hiddip–hip–hiddip: $\arccos \left({\frac {1}{3}}\right)\approx 70.52877^{\circ }$
Central density	1
Number of external pieces	14
Level of complexity	30
Related polytopes
Army	Hatut
Regiment	Hatut
Dual	Hexagonal-triakis tetrahedral duotegum
Conjugate	Hexagonal-truncated tetrahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A3×G2, order 288
Convex	Yes
Nature	Tame

The hexagonal-truncated tetrahedral duoprism or hatut is a convex uniform duoprism that consists of 6 truncated tetrahedral prisms, 4 hexagonal duoprisms, and 4 triangular-hexagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-hexagonal duoprism, and 2 hexagonal duoprisms.

Vertex coordinates

The vertices of a hexagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:

• $\left(\pm 1,\,0,\,{\frac {3{\sqrt {2}}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,{\frac {3{\sqrt {2}}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)$.

Representations

A hexagonal-truncated tetrahedral duoprism has the following Coxeter diagrams:

• x6o x3x3o () (full symmetry)
• x3x x3x3o () (hexagons as ditrigons)

External links

• Klitzing, Richard. "hatut".