Hexagonal-decagonal duoprism

Hexagonal-decagonal duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hadedip
Coxeter diagram	x6o x10o ()
Elements
Cells	10 hexagonal prisms, 6 decagonal prisms
Faces	60 squares, 10 hexagons, 6 decagons
Edges	60+60
Vertices	60
Vertex figure	Digonal disphenoid, edge lengths √3 (base 1), √(5+√5)/2 (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Hip–6–hip: 144°
	Dip–10–dip: 120°
	Dip–4–hip: 90°
Central density	1
Number of external pieces	16
Level of complexity	6
Related polytopes
Army	Hadedip
Regiment	Hadedip
Dual	Hexagonal-decagonal duotegum
Conjugate	Hexagonal-decagrammic duoprism
Abstract & topological properties
Flag count	1440
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2×I2(10), order 240
Flag orbits	6
Convex	Yes
Nature	Tame

The hexagonal-decagonal duoprism or hadedip, also known as the 6-10 duoprism, is a uniform duoprism that consists of 6 decagonal prisms and 10 hexagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a triangular-pentagonal duoantiprism, although it cannot be made uniform.

Gallery[edit | edit source]

Net

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a hexagonal-decagonal duoprism with edge length 1 are given by:

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