Octagrammic-dodecagrammic duoprism

Octagrammic-dodecagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x8/3o x12/5o ()
Elements
Cells	12 octagrammic prisms, 8 dodecagrammic prisms
Faces	96 squares, 12 octagrams, 8 dodecagrams
Edges	96+96
Vertices	96
Vertex figure	Digonal disphenoid, edge lengths √2–√2 (base 1), (√6–√2)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stop–4–stwip: 90°
	Stwip–12/5–stwip: 45°
	Stop–8/3–stop: 30°
Central density	15
Number of external pieces	40
Level of complexity	24
Related polytopes
Army	Semi-uniform otwadip
Dual	Octagrammic-dodecagrammic duotegum
Conjugates	Octagonal-dodecagonal duoprism, Octagonal-dodecagrammic duoprism, Octagrammic-dodecagonal duoprism
Abstract & topological properties
Flag count	2304
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)×I2(12), order 384
Convex	No
Nature	Tame

The octagrammic-dodecagrammic duoprism, also known as the 8/3-12/5 duoprism, is a uniform duoprism that consists of 12 octagrammic prisms and 8 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

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

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