Hexagonal-octagrammic duoprism

Hexagonal-octagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Histodip
Coxeter diagram	x6o x8/3o ()
Elements
Cells	8 hexagonal prisms, 6 octagrammic prisms
Faces	48 squares, 8 hexagons, 6 octagrams
Edges	48+48
Vertices	48
Vertex figure	Digonal disphenoid, edge lengths √3 (base 1), √2–√2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stop–8/3–stop: 120°
	Hip–4–stop: 90°
	Hip–6–hip: 45°
Central density	3
Number of external pieces	22
Level of complexity	12
Related polytopes
Army	Semi-uniform hodip, edge lengths 1 (hexagon), (octagon)
Regiment	Histodip
Dual	Hexagonal-octagrammic duotegum
Conjugate	Hexagonal-octagonal duoprism
Abstract & topological properties
Flag count	1152
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2×I2(8), order 192
Convex	No
Nature	Tame

The hexagonal-octagrammic duoprism, also known as histodip or the 6-8/3 duoprism, is a uniform duoprism that consists of 8 hexagonal prisms and 6 octagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a hexagonal-octagrammic duoprism, centered at the origin and with unit edge length, are given by:

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