Triangular-enneagrammic duoprism

Triangular-enneagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tastedip
Coxeter diagram	x3o x9/2o ()
Elements
Cells	9 triangular prisms, 3 enneagrammic prisms
Faces	9 triangles, 27 squares, 3 enneagrams
Edges	27+27
Vertices	27
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), 2cos(2π/9) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Trip–3–trip: 100°
	Trip–4–step: 90°
	Step–9/2–step: 60°
Height
Central density	2
Number of external pieces	21
Level of complexity	12
Related polytopes
Army	Semi-uniform tedip
Regiment	Tastedip
Dual	Triangular-enneagrammic duotegum
Conjugates	Triangular-enneagonal duoprism, Triangular-great enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(9), order 108
Convex	No
Nature	Tame

The triangular-enneagrammic duoprism, also known as tastedip or the 3-9/2 duoprism, is a uniform duoprism that consists of 9 triangular prisms and 3 enneagrammic prisms, with 2 of each at each vertex.

The name can also refer to the triangular-great enneagrammic duoprism.

Vertex coordinates[edit | edit source]

The coordinates of a triangular-enneagrammic duoprism, centered at the origin and with edge length 2sin(2π/9), are given by:

$\left(0,\,{\frac {2{\sqrt {3}}}{3}}\sin {\frac {2\pi }{9}},\,1,\,0\right),$
$\left(0,\,{\frac {2{\sqrt {3}}}{3}}\sin {\frac {2\pi }{9}},\,\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right)\right),$
$\left(0,\,{\frac {2{\sqrt {3}}}{3}}\sin {\frac {2\pi }{9}},\,-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$
$\left(\pm \sin {\frac {2\pi }{9}},\,-{\frac {\sqrt {3}}{3}}\sin {\frac {2\pi }{9}},\,1,\,0\right),$
$\left(\pm \sin {\frac {2\pi }{9}},\,-{\frac {\sqrt {3}}{3}}\sin {\frac {2\pi }{9}},\,\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right)\right),$
$\left(\pm \sin {\frac {2\pi }{9}},\,-{\frac {\sqrt {3}}{3}}\sin {\frac {2\pi }{9}},\,-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$