Triangular-decagrammic duoprism

Triangular-decagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tistadedip
Coxeter diagram	x3o x10/3o ()
Elements
Cells	10 triangular prisms, 3 decagrammic prisms
Faces	10 triangles, 30 squares, 3 decagrams
Edges	30+30
Vertices	30
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), √5–√5/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Trip–4–stiddip: 90°
	Trip–3–trip: 72°
	Stiddip–10/3–stiddip: 60°
Height
Central density	3
Number of external pieces	13
Level of complexity	12
Related polytopes
Army	Semi-uniform tradedip
Regiment	Tistadedip
Dual	Triangular-decagrammic duotegum
Conjugate	Triangular-decagonal duoprism
Abstract & topological properties
Flag count	720
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(10), order 120
Convex	No
Nature	Tame

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

Vertex coordinates[edit | edit source]

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

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