Octagonal-octahedral duoprism

Octagonal-octahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Owoct
Coxeter diagram	x8o o4o3x ()
Elements
Tera	8 octahedral prisms, 8 triangular-octagonal duoprisms
Cells	64 triangular prisms, 8 octahedra, 12 octagonal prisms
Faces	64 triangles, 96 squares, 6 octagons
Edges	48+96
Vertices	48
Vertex figure	Square scalene, edge lengths 1 (base square), √2+√2 (top), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563$
Hypervolume	${\frac {4+2{\sqrt {2}}}{3}}\approx 2.27614$
Diteral angles	Ope–oct–ope: 135°
	Todip–op–todip: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	Todip–trip–ope: 90°
	${\frac {\sqrt {6}}{3}}\approx 0.81650$
Central density	1
Number of external pieces	16
Level of complexity	10
Related polytopes
Army	Owoct
Regiment	Owoct
Dual	Octagonal-cubic duotegum
Conjugate	Octagrammic-octahedral duoprism
Abstract & topological properties
Flag count	7680
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×I2(8), order 768
Convex	Yes
Nature	Tame

The octagonal-octahedral duoprism or owoct is a convex uniform duoprism that consists of 8 octahedral prisms and 8 triangular-octagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-octagonal duoprisms.

Vertex coordinates

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

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

Representations

An octagonal-octahedral duoprism has the following Coxeter diagrams:

• x8o o4o3x () (full symmetry)
• x4x o4o3x () (octagons as ditetragons)
• x8o o3x3o () (octahedra as tetratetrahedra)
• x4x o3x3o () (octagons as ditetragons and octahedra as tetratetrahedra)
• xo3ox xx8oo&#x (triangular-octagonal duoprism atop triangle-gyrated triangular-octagonal duoprism)

External links

• Klitzing, Richard. "owoct".