Decagonal-great hendecagrammic duoprism

Decagonal-great hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x10o x11/4o ()
Elements
Cells	11 decagonal prisms, 10 great hendecagrammic prisms
Faces	110 squares, 11 decagons, 10 great hendecagrams
Edges	110+110
Vertices	110
Vertex figure	Digonal disphenoid, edge lengths √(5+√5)/2 (base 1), 2cos(4π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {3+{\sqrt {5}}}{2}}+{\frac {1}{4\sin ^{2}{\frac {4\pi }{11}}}}}}\approx 1.70885$
Hypervolume	$55{\frac {\sqrt {5+2{\sqrt {5}}}}{8\tan {\frac {4\pi }{11}}}}\approx 9.66303$
Dichoral angles	Gashenp–11/4–gashenp: 144°
	Dip–4–gashenp: 90°
	Dip–10–dip: ${\frac {3\pi }{11}}\approx 49.09091^{\circ }$
Central density	4
Number of external pieces	32
Level of complexity	12
Related polytopes
Army	Semi-uniform dahendip
Dual	Decagonal-great hendecagrammic duotegum
Conjugates	Decagonal-hendecagonal duoprism, Decagonal-small hendecagrammic duoprism, Decagonal-hendecagrammic duoprism, Decagonal-grand hendecagrammic duoprism, Decagrammic-hendecagonal duoprism, Decagrammic-small hendecagrammic duoprism, Decagrammic-hendecagrammic duoprism, Decagrammic-great hendecagrammic duoprism, Decagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(10)×I2(11), order 440
Convex	No
Nature	Tame

The decagonal-great hendecagrammic duoprism, also known as the 10-11/4 duoprism, is a uniform duoprism that consists of 11 decagonal prisms and 10 great hendecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

The coordinates of a decagonal-great hendecagrammic duoprism, centered at the origin and with edge length 2sin(4π/11), are given by:

• $\left(\pm \sin {\frac {4\pi }{11}},\,\pm {\sqrt {5+2{\sqrt {5}}}}\sin {\frac {4\pi }{11}},\,1,\,0\right)$,
• $\left(\pm \sin {\frac {4\pi }{11}},\,\pm {\sqrt {5+2{\sqrt {5}}}}\sin {\frac {4\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right)$,
• $\left(\pm {\frac {3+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{11}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{2}}}\sin {\frac {4\pi }{11}},\,1,\,0\right)$,
• $\left(\pm {\frac {3+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{11}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{2}}}\sin {\frac {4\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right)$,
• $\left(\pm \left(1+{\sqrt {5}}\right)\sin {\frac {4\pi }{11}},\,0,\,1,\,0\right)$,
• $\left(\pm \left(1+{\sqrt {5}}\right)\sin {\frac {4\pi }{11}},\,0,\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right)$,

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

Representations

A decagonal-great hendecagrammic duoprism has the following Coxeter diagrams:

• x10o x11/4o () (full symmetry)
• x5x x11/4o () (H₂×I₂(11) symmetry, decagons as dipentagons)

External links

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

• Klitzing, Richard. "nd-mb-dip".