Square-great hendecagrammic duoprism

Square-great hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x4o x11/4o ()
Elements
Cells	11 cubes, 4 great hendecagrammic prisms
Faces	11+44 squares, 4 great hendecagrams
Edges	44+44
Vertices	44
Vertex figure	Digonal disphenoid, edge lengths 2cos(4π/11) (base 1) and √2 (base 2 and sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2+{\frac {1}{\sin ^{2}{\frac {4\pi }{11}}}}}}{2}}\approx 0.89562$
Hypervolume	${\frac {11}{4\tan {\frac {4\pi }{11}}}}\approx 1.25588$
Dichoral angles	Gishenp–11/4–gishenp: 90°
	Cube–4–gishenp: 90°
	Cube–4–cube: ${\frac {3\pi }{11}}\approx 49.09091^{\circ }$
Height	1
Central density	4
Number of external pieces	26
Level of complexity	12
Related polytopes
Army	Semi-uniform shendip
Dual	Square-great hendecagrammic duotegum
Conjugates	Square-hendecagonal duoprism, Square-small hendecagrammic duoprism, Square-hendecagrammic duoprism, Square-grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2×I2(11), order 176
Convex	No
Nature	Tame

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

Vertex coordinates

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

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

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

Representations

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

• x4o x11/4o (full symmetry)
• x x x11/4o () (I₂(11)×A₁×A₁ symmetry, great hendecagrammic prismatic prism)

External links

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

• Klitzing, Richard. "nd-mb-dip".