Octagonal-grand hendecagrammic duoprism

Octagonal-grand hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x8o x11/5o ()
Elements
Cells	11 octagonal prisms, 8 grand hendecagrammic prisms
Faces	88 squares, 11 octagons, 8 grand hendecagrams
Edges	88+88
Vertices	88
Vertex figure	Digonal disphenoid, edge lengths √2+√2 (base 1), 2cos(5π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {2+{\sqrt {2}}}{2}}+{\frac {1}{4\sin ^{2}{\frac {5\pi }{11}}}}}}\approx 1.40081$
Hypervolume	$11{\frac {1+{\sqrt {2}}}{2\tan {\frac {5\pi }{11}}}}\approx 1.90911$
Dichoral angles	Gashenp–11/5–gashenp: 135°
	Op–4–gashenp: 90°
	Op–8–op: ${\frac {\pi }{11}}\approx 16.36364^{\circ }$
Central density	5
Number of external pieces	30
Level of complexity	12
Related polytopes
Army	Semi-uniform ohendip
Dual	Octagonal-grand hendecagrammic duotegum
Conjugates	Octagonal-hendecagonal duoprism, Octagonal-small hendecagrammic duoprism, Octagonal-hendecagrammic duoprism, Octagonal-great hendecagrammic duoprism, Octagrammic-hendecagonal duoprism, Octagrammic-small hendecagrammic duoprism, Octagrammic-hendecagrammic duoprism, Octagrammic-great hendecagrammic duoprism, Octagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)×I2(11), order 352
Convex	No
Nature	Tame

The octagonal-grand hendecagrammic duoprism, also known as the 8/11-5 duoprism, is a uniform duoprism that consists of 11 octagonal prisms and 8 grand hendecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

The coordinates of an octagonal-grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by:

• $\left(\pm \sin {\frac {5\pi }{11}},\,\pm \left(1+{\sqrt {2}}\right)\sin {\frac {5\pi }{11}},\,1,\,0\right),$
• $\left(\pm \sin {\frac {5\pi }{11}},\,\pm \left(1+{\sqrt {2}}\right)\sin {\frac {5\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right),$
• $\left(\pm \left(1+{\sqrt {2}}\right)\sin {\frac {5\pi }{11}},\,\pm \sin {\frac {5\pi }{11}},\,1,\,0\right),$
• $\left(\pm \left(1+{\sqrt {2}}\right)\sin {\frac {5\pi }{11}},\,\pm \sin {\frac {5\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right),$

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

Representations

An octagonal-grand hendecagrammic duoprism has the following Coxeter diagrams:

• x8o x11/5o (full symmetry)
• x4x x11/5o () (BC₂×I₂(11) symmetry, octagons as ditetragons)

External links

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

• Klitzing, Richard. "nd-mb-dip".