# Hendecagonal-hendecagrammic duoprism

Hendecagonal-hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11o x11/3o ()
Elements
Cells11 hendecagonal prisms, 11 hendecagrammic prisms
Faces121 squares, 11 hendecagons, 11 hendecagrams
Edges121+121
Vertices121
Vertex figureDigonal disphenoid, edge lengths 2cos(π/11) (base 1), 2cos(3π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}+{\frac {1}{4\sin ^{2}{\frac {3\pi }{11}}}}}}\approx 1.89404}$
Hypervolume${\displaystyle {\frac {121}{16\tan {\frac {\pi }{11}}\tan {\frac {3\pi }{11}}}}\approx 22.31728}$
Dichoral anglesShenp–11/3–shenp: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Henp–4–shenp: 90°
Henp–11–henp: ${\displaystyle {\frac {5\pi }{11}}\approx 81.81818^{\circ }}$
Central density3
Number of external pieces33
Level of complexity12
Related polytopes
ArmySemi-uniform handip
DualHendecagonal-hendecagrammic duotegum
ConjugatesHendecagonal-small hendecagrammic duoprism, Hendecagonal-great hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-hendecagrammic duoprism, Small hendecagrammic-great hendecagrammic duoprism, Small hendecagrammic-grand hendecagrammic duoprism, Hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Flag count2904
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)×I2(11), order 484
ConvexNo
NatureTame

The hendecagonal-hendecagrammic duoprism, also known as the 11-11/3 duoprism, is a uniform duoprism that consists of 11 hendecagonal prisms and 11 hendecagrammic prisms, with 2 of each at each vertex.

The name can also refer to the hendecagonal-small hendecagrammic duoprism, the hendecagonal-great hendecagrammic duoprism, or the hendecagonal-grand hendecagrammic duoprism.

## Vertex coordinates

The coordinates of a hendecagonal-hendecagrammic duoprism, centered at the origin and with edge length 4sin(π/11)sin(3π/11), are given by:

• ${\displaystyle \left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {3\pi }{11}},\,0\right)}$,
• ${\displaystyle \left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {3\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {3\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right)}$,
• ${\displaystyle \left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {3\pi }{11}},\,0\right)}$,
• ${\displaystyle \left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {3\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {3\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right)}$,

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