Octagonal-truncated cubic duoprism

Octagonal-truncated cubic duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Otic
Coxeter diagram	x8o x4x3o
Elements
Tera	8 triangular-octagonal duoprisms, 8 truncated cubic prisms, 6 octagonal duoprisms
Cells	64 triangular prisms, 12+24+48 octagonal prisms, 8 truncated cubes
Faces	64 triangles, 96+192 squares, 24+48 octagons
Edges	96+192+192
Vertices	192
Vertex figure	Digonal disphenoidal pyramid, edge lengths 1, √2+√2, √2+√2 (base triangle), √2+√2 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\frac {3+{\sqrt {2}}}{2}}\approx 2.20711$
Hypervolume	$14{\frac {7+5{\sqrt {2}}}{3}}\approx 65.66498$
Diteral angles	Ticcup–tic–ticcup: 135°
	Todip–op–odip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Todip–trip–ticcup: 90°
	Odip–op–ticcup: 90°
	Odip–op–odip: 90°
Central density	1
Number of external pieces	22
Level of complexity	30
Related polytopes
Army	Otic
Regiment	Otic
Dual	Octagonal-triakis octahedral duotegum
Conjugate	Octagrammic-quasitruncated hexahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×I2(8), order 768
Convex	Yes
Nature	Tame

The octagonal-truncated cubic duoprism or otic is a convex uniform duoprism that consists of 8 truncated cubic prisms, 6 octagonal duoprisms, and 8 triangular-octagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-octagonal duoprism, and 2 octagonal duoprisms.

The octagonal-truncated cubic duoprism can be vertex-inscribed into a small rhombated penteract.

Vertex coordinates

The vertices of an octagonal-truncated cubic duoprism of edge length 1 are given by all permutations of the last three coordinates of:

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

Representations

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

• x8o x4x3o (full symmetry)
• x4x x4x3o (octagons as ditetragons)

External links

• Klitzing, Richard. "otic".