Octagonal-truncated tetrahedral duoprism

Octagonal-truncated tetrahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Otut
Coxeter diagram	x8o x3x3o
Elements
Tera	4 triangular-octagonal duoprisms, 8 truncated tetrahedral prisms, 4 hexagonal-octagonal duoprisms
Cells	32 triangular prisms, 32 hexagonal prisms, 8 truncated tetrahedra, 6+12 octagonal prisms
Faces	32 triangles, 48+96 squares, 32 hexagons, 12 octagons
Edges	48+96+96
Vertices	96
Vertex figure	Digonal disphenoidal pyramid, edge lengths 1, √3, √3 (base triangle), √2+√2 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {19+4{\sqrt {2}}}{8}}}\approx 1.75559$
Hypervolume	$23{\frac {2+{\sqrt {2}}}{6}}\approx 13.08782$
Diteral angles	Tuttip–tut–tuttip: 135°
	Todip-op-hodip: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	Todip–trip–tuttip: 90°
	Hodip-hip-tuttip: 90°
	Hodip–op–hodip: $\arccos \left({\frac {1}{3}}\right)\approx 70.52877^{\circ }$
Central density	1
Number of external pieces	16
Level of complexity	30
Related polytopes
Army	Otut
Regiment	Otut
Dual	Octagonal-triakis tetrahedral duotegum
Conjugate	Octagrammic-truncated tetrahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A3×I2(8), order 384
Convex	Yes
Nature	Tame

The octagonal-truncated tetrahedral duoprism or otut is a convex uniform duoprism that consists of 8 truncated tetrahedral prisms, 4 hexagonal-octagonal duoprisms, and 4 triangular-octagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-octagonal duoprism, and 2 hexagonal-octagonal duoprisms.

Vertex coordinates

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

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

Representations

An octagonal-truncated tetrahedral duoprism has the following Coxeter diagrams:

• x8o x3x3o (full symmetry)
• x4x x3x3o (octagons as ditetragons)

External links

• Klitzing, Richard. "otut".