Hexagonal-decagrammic duoprism

Hexagonal-decagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Histadedip
Coxeter diagram	x6o x10/3o ()
Elements
Cells	10 hexagonal prisms, 6 decagrammic prisms
Faces	60 squares, 10 hexagons, 6 decagrams
Edges	60+60
Vertices	60
Vertex figure	Digonal disphenoid, edge lengths √3 (base 1), √(5–√5)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stiddip–10/3–stiddip: 120°
	Hip–4–stiddip: 90°
	Hip–6–hip: 72°
Central density	3
Number of external pieces	26
Level of complexity	12
Related polytopes
Army	Semi-uniform hadedip
Regiment	Histadedip
Dual	Hexagonal-decagrammic duotegum
Conjugate	Hexagonal-decagonal duoprism
Abstract & topological properties
Flag count	1440
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2×I2(10), order 240
Convex	No
Nature	Tame

The hexagonal-decagrammic duoprism, also known as histadedip or the 6-10/3 duoprism, is a uniform duoprism that consists of 10 hexagonal prisms and 6 decagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

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

$\left(\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)$ ,
$\left(\pm 1,\,0,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)$ ,
$\left(\pm 1,\,0,\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)$ .