# Octagonal-truncated cubic duoprism

Octagonal-truncated cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymOtic
Coxeter diagramx8o x4x3o
Elements
Tera8 triangular-octagonal duoprisms, 8 truncated cubic prisms, 6 octagonal duoprisms
Cells64 triangular prisms, 12+24+48 octagonal prisms, 8 truncated cubes
Faces64 triangles, 96+192 squares, 24+48 octagons
Edges96+192+192
Vertices192
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 2+2, 2+2 (base triangle), 2+2 (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {3+{\sqrt {2}}}{2}}\approx 2.20711}$
Hypervolume${\displaystyle 14{\frac {7+5{\sqrt {2}}}{3}}\approx 65.66498}$
Diteral anglesTiccup–tic–ticcup: 135°
Todip–op–odip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Todip–trip–ticcup: 90°
Odip–op–ticcup: 90°
Odip–op–odip: 90°
Central density1
Number of external pieces22
Level of complexity30
Related polytopes
ArmyOtic
RegimentOtic
DualOctagonal-triakis octahedral duotegum
ConjugateOctagrammic-quasitruncated hexahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(8), order 768
ConvexYes
NatureTame

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:

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

## Representations

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

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