# Hendecagrammic duoprism

Hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramx11/3o x11/3o ()
Elements
Cells22 hendecagrammic prisms
Faces121 squares, 22 hendecagrams
Edges242
Vertices121
Vertex figureTetragonal disphenoid, edge lengths 2cos(3π/11) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt2}{2\sin\frac{3\pi}{11}} ≈ 0.93564}$
Inradius${\displaystyle \frac{1}{2\tan\frac{3\pi}{11}} ≈ 0.43325}$
Hypervolume${\displaystyle \frac{121}{16\tan^2\frac{3\pi}{11}} ≈ 5.67816}$
Dichoral anglesShenp–4–shenp: 90°
Shenp–11/3–shenp: ${\displaystyle \frac{5\pi}{11} ≈ 81.81818°}$
Central density9
Number of external pieces44
Level of complexity12
Related polytopes
ArmyHandip
DualHendecagrammic duotegum
ConjugatesHendecagonal duoprism, Small hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
ConvexNo
NatureTame

The hendecagrammic duoprism, also known as the hendecagrammic-hendecagrammic duoprism, the 11/3 duoprism or the 11/3-11/3 duoprism, is a noble uniform duoprism that consists of 22 hendecagrammic prisms, with 4 meeting at each vertex.

## Vertex coordinates

The coordinates of a hendecagrammic duoprism, centered at the origin and with edge length 2sin(3π/11), are given by:

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

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