Hexagonal-dodecagrammic duoprism

Hexagonal-dodecagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x6o x12/5o ()
Elements
Cells	12 hexagonal prisms, 6 dodecagrammic prisms
Faces	72 squares, 12 hexagons, 6 dodecagrams
Edges	72+72
Vertices	72
Vertex figure	Digonal disphenoid, edge lengths √3 (base 1), (√6–√2)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stwip–12/5–stwip: 120°
	Hip–4–stwip: 90°
	Hip–6–hip: 30°
Central density	5
Number of external pieces	30
Level of complexity	12
Related polytopes
Army	Semi-uniform hitwadip
Dual	Hexagonal-dodecagrammic duotegum
Conjugate	Hexagonal-dodecagonal duoprism
Abstract & topological properties
Flag count	1728
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2×I2(12), order 288
Convex	No
Nature	Tame

The hexagonal-dodecagrammic duoprism, also known as the 6-12/5 duoprism, is a uniform duoprism that consists of 12 hexagonal prisms and 6 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

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

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