Triangular-heptagonal duoprism

Triangular-heptagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Theddip
Coxeter diagram	x3o x7o ()
Elements
Cells	7 triangular prisms, 3 heptagonal prisms
Faces	7 triangles, 21 squares, 3 heptagons
Edges	21+21
Vertices	21
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), 2cos(π/7) (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {1}{3}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{7}}}}}}\approx 1.28892$
Hypervolume	${\frac {7{\sqrt {3}}}{16\tan {\frac {\pi }{7}}}}\approx 1.57353$
Dichoral angles	Trip–3–trip: ${\frac {5\pi }{7}}\approx 128.57143^{\circ }$
	Hep–4–trip: 90°
	Hep–7–hep: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	10
Level of complexity	6
Related polytopes
Army	Theddip
Regiment	Theddip
Dual	Triangular-heptagonal duotegum
Conjugates	Triangular-heptagrammic duoprism, Triangular-great heptagrammic duoprism
Abstract & topological properties
Flag count	504
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(7), order 84
Flag orbits	6
Convex	Yes
Nature	Tame

The triangular-heptagonal duoprism or theddip, also known as the 3-7 duoprism, is a uniform duoprism that consists of 3 heptagonal prisms and 7 triangular prisms, with 2 of each meeting at each vertex. It can also be seen as a convex segmentochoron, being a heptagon atop a heptagonal prism.

Gallery

• 
  Net

Vertex coordinates

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

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

where j = 2, 4, 6.

External links

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

• Klitzing, Richard. "n-m-dip".