Great enneagrammic-small hendecagrammic duoprism Rank 4 Type Uniform Notation Coxeter diagram x9/4o x11/2o ( ) Elements Cells 11 great enneagrammic prisms , 9 small hendecagrammic prisms Faces 99 squares , 11 great enneagrams , 9 small hendecagrams Edges 99+99 Vertices 99 Vertex figure Digonal disphenoid , edge lengths 2cos(4π/9) (base 1), 2cos(2π/11) (base 2), √2 (sides)Measures (edge length 1) Circumradius
1
4
sin
2
4
π
9
+
1
4
sin
2
2
π
11
≈
1.05503
{\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {4\pi }{9}}}}+{\frac {1}{4\sin ^{2}{\frac {2\pi }{11}}}}}}\approx 1.05503}
Hypervolume
99
16
tan
4
π
9
tan
2
π
11
≈
1.69767
{\displaystyle {\frac {99}{16\tan {\frac {4\pi }{9}}\tan {\frac {2\pi }{11}}}}\approx 1.69767}
Dichoral angles Gistep–9/4–gistep:
7
π
11
≈
114.54545
∘
{\displaystyle {\frac {7\pi }{11}}\approx 114.54545^{\circ }}
Gistep–4–sishenp: 90° Sishenp–11/2–sishenp: 20° Central density 8 Number of external pieces 40 Level of complexity 24 Related polytopes Army Semi-uniform ehendip Dual Great enneagrammic-small hendecagrammic duotegum Conjugates Enneagonal-hendecagonal duoprism , Enneagonal-small hendecagrammic duoprism , Enneagonal-hendecagrammic duoprism , Enneagonal-great hendecagrammic duoprism , Enneagonal-grand hendecagrammic duoprism , Enneagrammic-hendecagonal duoprism , Enneagrammic-small hendecagrammic duoprism , Enneagrammic-hendecagrammic duoprism , Enneagrammic-great hendecagrammic duoprism , Enneagrammic-grand hendecagrammic duoprism , Great enneagrammic-hendecagonal duoprism , Great enneagrammic-hendecagrammic duoprism , Great enneagrammic-great hendecagrammic duoprism , Great enneagrammic-grand hendecagrammic duoprism Abstract & topological properties Flag count2376 Euler characteristic 0 Orientable Yes Properties Symmetry I2 (9)×I2 (11) , order 396Convex No Nature Tame
The great enneagrammic-small hendecagrammic duoprism , also known as the 9/4-11/2 duoprism , is a uniform duoprism that consists of 11 great enneagrammic prisms and 9 small hendecagrammic prisms , with 2 of each at each vertex.
The vertex coordinates of a great enneagrammic-small hendecagrammic duoprism, centered at the origin and with edge length 4sin(4π/9)sin(2π/11), are given by:
(
2
sin
2
π
11
,
0
,
2
sin
4
π
9
,
0
)
{\displaystyle \left(2\sin {\frac {2\pi }{11}},\,0,\,2\sin {\frac {4\pi }{9}},\,0\right)}
,
(
2
sin
2
π
11
,
0
,
2
sin
4
π
9
cos
(
k
π
11
)
,
±
2
sin
4
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {2\pi }{11}},\,0,\,2\sin {\frac {4\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {4\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
,
(
2
sin
2
π
11
cos
(
j
π
9
)
,
±
2
sin
2
π
11
sin
(
j
π
9
)
,
2
sin
4
π
9
,
0
)
{\displaystyle \left(2\sin {\frac {2\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\,\pm 2\sin {\frac {2\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),\,2\sin {\frac {4\pi }{9}},\,0\right)}
,
(
2
sin
2
π
11
cos
(
j
π
9
)
,
±
2
sin
2
π
11
sin
(
j
π
9
)
,
2
sin
4
π
9
cos
(
k
π
11
)
,
±
2
sin
4
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {2\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\,\pm 2\sin {\frac {2\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),\,2\sin {\frac {4\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {4\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
,
(
−
sin
2
π
11
,
±
3
sin
2
π
11
,
2
sin
4
π
9
,
0
)
{\displaystyle \left(-\sin {\frac {2\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {2\pi }{11}},\,2\sin {\frac {4\pi }{9}},\,0\right)}
,
(
−
sin
2
π
11
,
±
3
sin
2
π
11
,
2
sin
4
π
9
cos
(
k
π
11
)
,
±
2
sin
4
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(-\sin {\frac {2\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {2\pi }{11}},\,2\sin {\frac {4\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {4\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
,
where j = 2, 4, 8 and k = 2, 4, 6, 8, 10.