Hendecagonalhendecagrammic duoprism 


Rank  4 

Type  Uniform 

Notation 

Coxeter diagram  x11o x11/3o () 

Elements 

Cells  11 hendecagonal prisms, 11 hendecagrammic prisms 

Faces  121 squares, 11 hendecagons, 11 hendecagrams 

Edges  121+121 

Vertices  121 

Vertex figure  Digonal disphenoid, edge lengths 2cos(π/11) (base 1), 2cos(3π/11) (base 2), √2 (sides) 

Measures (edge length 1) 

Circumradius  ${\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}+{\frac {1}{4\sin ^{2}{\frac {3\pi }{11}}}}}}\approx 1.89404$ 

Hypervolume  ${\frac {121}{16\tan {\frac {\pi }{11}}\tan {\frac {3\pi }{11}}}}\approx 22.31728$ 

Dichoral angles  Shenp–11/3–shenp: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$ 

 Henp–4–shenp: 90° 

 Henp–11–henp: ${\frac {5\pi }{11}}\approx 81.81818^{\circ }$ 

Central density  3 

Number of external pieces  33 

Level of complexity  12 

Related polytopes 

Army  Semiuniform handip 

Dual  Hendecagonalhendecagrammic duotegum 

Conjugates  Hendecagonalsmall hendecagrammic duoprism, Hendecagonalgreat hendecagrammic duoprism, Hendecagonalgrand hendecagrammic duoprism, Small hendecagrammichendecagrammic duoprism, Small hendecagrammicgreat hendecagrammic duoprism, Small hendecagrammicgrand hendecagrammic duoprism, Hendecagrammicgreat hendecagrammic duoprism, Hendecagrammicgrand hendecagrammic duoprism, Great hendecagrammicgrand hendecagrammic duoprism 

Abstract & topological properties 

Flag count  2904 

Euler characteristic  0 

Orientable  Yes 

Properties 

Symmetry  I_{2}(11)×I_{2}(11), order 484 

Convex  No 

Nature  Tame 

The hendecagonalhendecagrammic duoprism, also known as the 1111/3 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 hendecagonalsmall hendecagrammic duoprism, the hendecagonalgreat hendecagrammic duoprism, or the hendecagonalgrand hendecagrammic duoprism.
The coordinates of a hendecagonalhendecagrammic duoprism, centered at the origin and with edge length 4sin(π/11)sin(3π/11), are given by:
 $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {3\pi }{11}},\,0\right)$,
 $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {3\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {3\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right)$,
 $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {3\pi }{11}},\,0\right)$,
 $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {3\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {3\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right)$,
where j, k = 2, 4, 6, 8, 10.