Hexagonal-hendecagonal duoprism

Hexagonal-hendecagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hahendip
Coxeter diagram	x6o x11o ()
Elements
Cells	11 hexagonal prisms, 6 hendecagonal prisms
Faces	66 squares, 11 hexagons, 6 hendecagons
Edges	66+66
Vertices	66
Vertex figure	Digonal disphenoid, edge lengths √3 (base 1), 2cos(π/11) (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {4+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.03708$
Hypervolume	${\frac {33{\sqrt {3}}}{8\tan {\frac {\pi }{11}}}}\approx 24.33265$
Dichoral angles	Hip–6–hip: ${\frac {8\pi }{11}}\approx 147.27273^{\circ }$
	Henp–11–Henp: 120°
	Hip–4–henp: 90°
Central density	1
Number of external pieces	17
Level of complexity	6
Related polytopes
Army	Hahendip
Regiment	Hahendip
Dual	Hexagonal-hendecagonal duotegum
Conjugates	Hexagonal-small hendecagrammic duoprism, Hexagonal-hendecagrammic duoprism, Hexagonal-great hendecagrammic duoprism, Hexagonal-grand hendecagrammic duoprism
Abstract & topological properties
Flag count	1584
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2×I2(11), order 264
Convex	Yes
Nature	Tame

The hexagonal-hendecagonal duoprism or hahendip, also known as the 6-11 duoprism, is a uniform duoprism that consists of 6 hendecagonal prisms and 11 hexagonal prisms, with two of each joining at each vertex.

Vertex coordinates

The coordinates of a hexagonal-hendecagonal duoprism, centered at the origin and with edge length 2sin(π/11), are given by:

• $\left(\pm 2\sin {\frac {\pi }{11}},0,1,0\right)$,
• $\left(\pm 2\sin {\frac {\pi }{11}},0,\cos \left({\frac {j\pi }{11}}\right),\pm \sin \left({\frac {j\pi }{11}}\right)\right)$,
• $\left(\pm \sin {\frac {\pi }{11}},\pm {\sqrt {3}}\sin {\frac {\pi }{11}},1,0\right)$,
• $\left(\pm \sin {\frac {\pi }{11}},\pm {\sqrt {3}}\sin {\frac {\pi }{11}},\cos \left({\frac {j\pi }{11}}\right),\pm \sin \left({\frac {j\pi }{11}}\right)\right)$,

where j = 2, 4, 6, 8, 10.

Representations

A hexagonal-hendecagonal duoprism has the following Coxeter diagrams:

• x6o x11o () (full symmetry)
• x3x x11o () (hexagons as ditrigons)

External links

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

• Klitzing, Richard. "n-m-dip".