Decagonal-icosahedral duoprism

Decagonal-icosahedral duoprism
	(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Dike
Coxeter diagram	x10o o5o3x ()
Elements
Tera	20 triangular-decagonal duoprisms, 10 icosahedral prisms
Cells	200 triangular prisms, 30 decagonal prisms, 10 icosahedra
Faces	200 triangles, 300 squares, 12 decagons
Edges	120+300
Vertices	120
Vertex figure	Pentagonal scalene, edge lengths 1 (base pentagon), √(5+√5)/2 (top), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral angles	Ipe–ike–ipe: 144°
	Tradedip–dip–tradedip:
	Tradedip–trip–ipe: 90°
Central density	1
Number of external pieces	30
Level of complexity	10
Related polytopes
Army	Dike
Regiment	Dike
Dual	Decagonal-dodecahedral duotegum
Conjugate	Decagrammic-great icosahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	H3×I2(10), order 2400
Convex	Yes
Nature	Tame

The decagonal-icosahedral duoprism or dike is a convex uniform duoprism that consists of 10 icosahedral prisms and 20 triangular-decagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-decagonal duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a triangular-icosahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:

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

A decagonal-icosahedral duoprism has the following Coxeter diagrams: