Triangular-decagonal duoprism

Triangular-decagonal duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tradedip
Coxeter diagram	x3o x10o ()
Elements
Cells	10 triangular prisms, 3 decagonal prisms
Faces	10 triangles, 30 squares, 3 decagons
Edges	30+30
Vertices	30
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), √(5+√5)/2 (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Trip–3–trip: 144°
	Trip–4–dip: 90°
	Dip–10–dip: 60°
Height
Central density	1
Number of external pieces	13
Level of complexity	6
Related polytopes
Army	Tradedip
Regiment	Tradedip
Dual	Triangular-decagonal duotegum
Conjugate	Triangular-decagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(10), order 120
Convex	Yes
Nature	Tame

The triangular-decagonal duoprism or tradedip, also known as the 3-10 duoprism, is a uniform duoprism that consists of 3 decagonal prisms and 10 triangular prisms, with 2 of each at each vertex.

It is also a CRF segmentochoron, being decagon atop decagonal prism. It is designated K-4.94 on Richard Klitzing's list.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triangular–decagonal duoprism of edge length 1, centered at the origin, are given by:

$\left(0,\,{\frac {\sqrt {3}}{3}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),$
$\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),$
$\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}}\right),$
$\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}}\right),$