# Square-hendecagonal duoprism

Square-hendecagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymShendip
Coxeter diagramx4o x11o ()
Elements
Cells11 cubes, 4 hendecagonal prisms
Faces11+44 squares, 4 hendecagons
Edges44+44
Vertices44
Vertex figureDigonal disphenoid, edge lengths 2cos(π/11) (base 1) and 2 (base 2 and sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 1.91041}$
Hypervolume${\displaystyle {\frac {11}{4\tan {\frac {\pi }{11}}}}\approx 9.36564}$
Dichoral anglesCube–4–cube: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Henp–11–henp: 90°
Henp–4–cube: 90°
Height1
Central density1
Number of external pieces15
Level of complexity6
Related polytopes
ArmyShendip
RegimentShendip
DualSquare-hendecagonal duotegum
ConjugatesSquare-small hendecagrammic duoprism,
Square-hendecagrammic duoprism,
Square-great hendecagrammic duoprism,
Square-grand hendecagrammic duoprism
Abstract & topological properties
Flag count1056
Euler characteristic0
OrientableYes
Properties
SymmetryB2×I2(11), order 176
Flag orbits6
ConvexYes
NatureTame

The square-hendecagonal duoprism or shendip, also known as the 4-11 duoprism, is a uniform duoprism that consists of 4 hendecagonal prisms and 11 cubes, with two of each joining at each vertex. It is also a convex segmentochoron, being the prism of the hendecagonal prism.

## Vertex coordinates

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

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

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

## Representations

A square-hendecagonal duoprism has the following Coxeter diagrams:

• x4o x11o () (full symmetry)
• x x x11o () (I2(11)×K2 symmetry, squares as rectangles)