Triangular-great heptagrammic duoprism

Triangular-great heptagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tagishdip
Coxeter diagram	x3o x7/3o ()
Elements
Cells	7 triangular prisms, 3 great heptagrammic prisms
Faces	7 triangles, 21 squares, 3 great heptagrams
Edges	21+21
Vertices	21
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), 2cos(3π/7) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {1}{3}}+{\frac {1}{4\sin ^{2}{\frac {3\pi }{7}}}}}}\approx 0.77224$
Hypervolume	${\frac {7{\sqrt {3}}}{16\tan {\frac {3\pi }{7}}}}\approx 0.17296$
Dichoral angles	Trip–4–giship: 90°
	Giship–7/3–giship: 60°
	Trip–3–trip: ${\frac {\pi }{7}}\approx 25.71429^{\circ }$
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	3
Number of external pieces	17
Level of complexity	12
Related polytopes
Army	Semi-uniform theddip
Regiment	Tagishdip
Dual	Triangular-great heptagrammic duotegum
Conjugates	Triangular-heptagonal duoprism, Triangular-heptagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(7), order 84
Convex	No
Nature	Tame

The triangular-great heptagrammic duoprism, also known as tagishdip or the 3-7/3 duoprism, is a uniform duoprism that consists of 3 great heptagrammic prisms and 7 triangular prisms, with two of each at each vertex.

Vertex coordinates

The coordinates of a triangular-great heptagrammic duoprism, centered at the origin and with edge length 2sin(3π/7), are given by:

• $\left(0,\,{\frac {2{\sqrt {3}}}{3}}\sin {\frac {3\pi }{7}},\,1,\,0\right),$
• $\left(0,\,{\frac {2{\sqrt {3}}}{3}}\sin {\frac {3\pi }{7}},\,\cos \left({\frac {j\pi }{7}}\right),\,\pm \sin \left({\frac {j\pi }{7}}\right)\right),$
• $\left(\pm \sin {\frac {3\pi }{7}},\,-{\frac {\sqrt {3}}{3}}\sin {\frac {3\pi }{7}},\,1,\,0\right),$
• $\left(\pm \sin {\frac {3\pi }{7}},\,-{\frac {\sqrt {3}}{3}}\sin {\frac {3\pi }{7}},\,\cos \left({\frac {j\pi }{7}}\right),\,\pm \sin \left({\frac {j\pi }{7}}\right)\right),$

where j = 2, 4, 6.

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "nd-mb-dip".