Triangular-truncated tetrahedral duoprism

Triangular-truncated tetrahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Tratut
Coxeter diagram	x3o x3x3o ()
Elements
Tera	4 triangular duoprisms, 4 triangular-hexagonal duoprisms, 3 truncated tetrahedral prisms
Cells	6+12+12 triangular prisms, 12 hexagonal prisms, 3 truncated tetrahedra
Faces	12+12 triangles, 18+36 squares, 12 hexagons
Edges	18+36+36
Vertices	36
Vertex figure	Digonal disphenoidal pyramid, edge lengths 1, √3, √3 (base triangle), 1 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{246}}{12} \approx 1.30703$
Hypervolume	$\frac{23\sqrt{6}}{48} \approx 1.17371$
Diteral angles	Triddip-trip-thiddip: $\arccos\left(-\frac13\right) \approx 109.47122^\circ$
	Triddip–trip–tuttip: 90°
	Thiddip-hip-tuttip: 90°
	Thiddip–trip–thiddip: $\arccos\left(\frac13\right) \approx 70.52877^\circ$
	Tuttip–tut–tuttip: 60°
Height	$\frac{\sqrt3}2 \approx 0.86603$
Central density	1
Related polytopes
Army	Tratut
Regiment	Tratut
Dual	Triangular-triakis tetrahedral duotegum
Conjugate	Triangular-truncated tetrahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A2×A3, order 144
Convex	Yes
Nature	Tame

The triangular-truncated tetrahedral duoprism or tratut is a convex uniform duoprism that consists of 3 truncated tetrahedral prisms, 4 triangular-hexagonal duoprisms, and 4 triangular duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular duoprism, and 2 triangular-hexagonal duoprisms. It is a duoprism based on a triangle and a truncated tetrahedron, which makes it a convex segmentoteron.

Vertex coordinates

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

• $\left(0,\,\frac{\sqrt3}3,\,\frac{3\sqrt2}4,\,\frac{\sqrt2}4,\,\frac{\sqrt2}4\right)$,
• $\left(\pm\frac12,\,-\frac{\sqrt3}6,\,\frac{3\sqrt2}4,\,\frac{\sqrt2}4,\,\frac{\sqrt2}4\right)$.

Representations

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

• x3o x3x3o () (full symmetry)
• ox oo3xx3xx&#x (tut atop tuttip)
• ooo3xxx3xxx&#x

External links

• Klitzing, Richard. "tratut".