Small hendecagrammic-grand hendecagrammic duoprism Rank 4 Type Uniform Notation Coxeter diagram x11/2o x11/5o ( Elements Cells 11 small hendecagrammic prisms , 11 grand hendecagrammic prisms Faces 121 squares , 11 small hendecagrams , 11 grand hendecagrams Edges 121+121 Vertices 121 Vertex figure Digonal disphenoid , edge lengths 2cos(2π/11) (base 1), 2cos(5π/11) (base 2), √2 (sides)Measures (edge length 1) Circumradius
1
4
sin
2
2
π
11
+
1
4
sin
2
5
π
11
≈
1.05379
{\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {2\pi }{11}}}}+{\frac {1}{4\sin ^{2}{\frac {5\pi }{11}}}}}}\approx 1.05379}
Hypervolume
121
16
tan
2
π
11
tan
5
π
11
≈
1.69191
{\displaystyle {\frac {121}{16\tan {\frac {2\pi }{11}}\tan {\frac {5\pi }{11}}}}\approx 1.69191}
Dichoral angles Gashenp–11/5–gashenp:
7
π
11
≈
114.54545
∘
{\displaystyle {\frac {7\pi }{11}}\approx 114.54545^{\circ }}
Sishenp–4–gashenp: 90° Sishenp–11/2–sishenp:
π
11
≈
16.36364
∘
{\displaystyle {\frac {\pi }{11}}\approx 16.36364^{\circ }}
Central density 10 Number of external pieces 44 Level of complexity 24 Related polytopes Army Semi-uniform handip Dual Small hendecagrammic-grand hendecagrammic duotegum Conjugates Hendecagonal-small hendecagrammic duoprism , Hendecagonal-hendecagrammic duoprism , Hendecagonal-great hendecagrammic duoprism , Hendecagonal-grand hendecagrammic duoprism , Small hendecagrammic-hendecagrammic duoprism , Small hendecagrammic-great hendecagrammic duoprism , Hendecagrammic-great hendecagrammic duoprism , Hendecagrammic-grand hendecagrammic duoprism , Great hendecagrammic-grand hendecagrammic duoprism Abstract & topological properties Euler characteristic 0 Orientable Yes Properties Symmetry I2 (11)×I2 (11) , order 484Convex No Nature Tame
The small hendecagrammic-grand hendecagrammic duoprism , also known as the 11/2-11/5 duoprism , is a uniform duoprism that consists of 11 small hendecagrammic prisms and 11 grand hendecagrammic prisms , with 2 of each at each vertex.
The vertex coordinates of a small hendecagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 4sin(2π/11)sin(5π/11), are given by:
(
2
sin
5
π
11
,
0
,
2
sin
2
π
11
,
0
)
,
{\displaystyle \left(2\sin {\frac {5\pi }{11}},\,0,\,2\sin {\frac {2\pi }{11}},\,0\right),}
(
2
sin
5
π
11
,
0
,
2
sin
2
π
11
cos
(
k
π
11
)
,
±
2
sin
2
π
11
sin
(
k
π
11
)
)
,
{\displaystyle \left(2\sin {\frac {5\pi }{11}},\,0,\,2\sin {\frac {2\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right),}
(
2
sin
5
π
11
cos
(
j
π
11
)
,
±
2
sin
5
π
11
sin
(
j
π
11
)
,
2
sin
2
π
11
,
0
)
,
{\displaystyle \left(2\sin {\frac {5\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {5\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {2\pi }{11}},\,0\right),}
(
2
sin
5
π
11
cos
(
j
π
11
)
,
±
2
sin
5
π
11
sin
(
j
π
11
)
,
2
sin
2
π
11
cos
(
k
π
11
)
,
±
2
sin
2
π
11
sin
(
k
π
11
)
)
,
{\displaystyle \left(2\sin {\frac {5\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {5\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {2\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right),}
where j , k = 2, 4, 6, 8, 10.
