# Hendecagonal duoprismatic prism

Hendecagonal duoprismatic prism
Rank5
TypeUniform
Notation
Bowers style acronymHenhenip
Coxeter diagramx x11o x11o
Elements
Tera22 square-hendecagonal duoprisms, 2 hendecagonal duoprisms
Cells121 cubes, 22+44 hendecagonal prisms
Faces242+242 squares, 44 hendecagons
Edges121+484
Vertices242
Vertex figureTetragonal disphenoidal pyramid, edge lengths 2cos(π/11) (disphenoid bases) and 2 (remaining edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {1+{\frac {2}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.55917}$
Hypervolume${\displaystyle {\frac {121}{16\tan ^{2}{\frac {\pi }{11}}}}\approx 87.71521}$
Diteral anglesShendip–henp–shendip: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Shendip–cube–shendip: 90°
Handip–henp–shendip: 90°
Height1
Central density1
Number of external pieces24
Level of complexity15
Related polytopes
ArmyHenhenip
RegimentHenhenip
DualHendecagonal duotegmatic tegum
ConjugatesSmall hendecagrammic duoprismatic prism, Hendecagrammic duoprismatic prism, Great hendecagrammic duoprismatic prism, Grand hendecagrammic duoprismatic prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryI2(11)≀S2×A1, order 1936
ConvexYes
NatureTame

The hendecagonal duoprismatic prism or henhenip, also known as the hendecagonal-hendecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 hendecagonal duoprisms and 22 square-hendecagonal duoprisms. Each vertex joins 4 square-hendecagonal duoprisms and 1 hendecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

## Vertex coordinates

The vertices of a hendecagonal duoprismatic prism of edge length 2sin(π/11) are given by:

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

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

## Representations

A hendecagonal duoprismatic prism has the following Coxeter diagrams:

• x x11o x11o (full symmetry)
• xx11oo xx11oo&#x (hendecagonal duoprism atop hendecagonal duoprism)