Triangular-truncated octahedral duoprism

Triangular-truncated octahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Tratoe
Coxeter diagram	x3o o4x3x ()
Elements
Tera	6 triangular-square duoprisms, 8 triangular-hexagonal duoprisms, 3 truncated octahedral prisms
Cells	12+24 triangular prisms, 18 cubes, 24 hexagonal prisms, 3 truncated octahedra
Faces	24 triangles, 18+36+72 squares, 24 hexagons
Edges	36+72+72
Vertices	72
Vertex figure	Digonal disphenoidal pyramid, edge lengths √2, √3, √3 (base triangle), 1 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {102}}{6}}\approx 1.68325$
Hypervolume	$2{\sqrt {6}}\approx 4.89898$
Diteral angles	Tisdip–trip–thiddip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Thiddip–trip–thiddip: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	Tisdip–cube–tope: 90°
	Thiddip–hip–tope: 90°
	Tope–toe–tope: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	17
Level of complexity	30
Related polytopes
Army	Tratoe
Regiment	Tratoe
Dual	Triangular-tetrakis hexahedral duotegum
Conjugate	None
Abstract & topological properties
Flag count	8640
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×A2, order 288
Convex	Yes
Nature	Tame

The triangular-truncated octahedral duoprism or tratoe is a convex uniform duoprism that consists of 3 truncated octahedral prisms, 8 triangular-hexagonal duoprisms, and 6 triangular-square duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 triangular-square duoprism, and 2 triangular-hexagonal duoprisms. It is a duoprism based on a triangle and a truncated octahedron, which makes it a convex segmentoteron.

Vertex coordinates

The vertices of a triangular-truncated octahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

• $\left(0,\,{\frac {\sqrt {3}}{3}},\,0,\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\sqrt {2}}\right),$
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,0,\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\sqrt {2}}\right).$

Representations

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

• x3o o4x3x (full symmetry)
• x3o x3x3x
• ox xx3xx3xx&#x (truncated octahedron atop truncated octahedral prism)
• xxx3xxx3xxx&#x

External links

• Klitzing, Richard. "tratoe".