Octagrammic-grand hendecagrammic duoprism

Octagrammic-grand hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x8/3o x11/5o ()
Elements
Cells	11 octagrammic prisms, 8 grand hendecagrammic prisms
Faces	88 squares, 11 octagrams, 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	${\sqrt {{\frac {2-{\sqrt {2}}}{2}}+{\frac {1}{4\sin ^{2}{\frac {5\pi }{11}}}}}}\approx 0.74031$
Hypervolume	$11{\frac {{\sqrt {2}}-1}{2\tan {\frac {5\pi }{11}}}}\approx 0.32755$
Dichoral angles	Stop–4–gashenp: 90°
	Gashenp–11/5–gashenp: 45°
	Stop–8/3–stop: ${\frac {\pi }{11}}\approx 16.36364^{\circ }$
Central density	15
Number of external pieces	38
Level of complexity	24
Related polytopes
Army	Semi-uniform ohendip
Dual	Octagrammic-grand hendecagrammic duotegum
Conjugates	Octagonal-hendecagonal duoprism, Octagonal-small hendecagrammic duoprism, Octagonal-hendecagrammic duoprism, Octagonal-great hendecagrammic duoprism, Octagonal-grand hendecagrammic duoprism, Octagrammic-hendecagonal duoprism, Octagrammic-small hendecagrammic duoprism, Octagrammic-hendecagrammic duoprism, Octagrammic-great hendecagrammic duoprism
Abstract & topological properties
Flag count	2112
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)×I2(11), order 352
Convex	No
Nature	Tame

The octagrammic-grand hendecagrammic duoprism, also known as the 8/3-11/5 duoprism, is a uniform duoprism that consists of 11 octagrammic prisms and 8 grand hendecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

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

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

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

Representations

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

• x8/3o x11/5o () (full symmetry)
• x4/3x x11/5o () (B₂×I₂(11) symmetry, octagrams as ditetragrams)

External links

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

• Klitzing, Richard. "nd-mb-dip".