Enneagrammic-great hendecagrammic duoprism Rank 4 Type Uniform Notation Coxeter diagram x9/2o x11/4o ( Elements Cells 11 enneagrammic prisms , 9 great hendecagrammic prisms Faces 99 squares , 11 enneagrams , 9 great hendecagrams Edges 99+99 Vertices 99 Vertex figure Digonal disphenoid , edge lengths 2cos(2π/9) (base 1), 2cos(4π/11) (base 2), √2 (sides)Measures (edge length 1) Circumradius
1
4
sin
2
2
π
9
+
1
4
sin
2
4
π
11
≈
0.95248
{\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {2\pi }{9}}}}+{\frac {1}{4\sin ^{2}{\frac {4\pi }{11}}}}}}\approx 0.95248}
Hypervolume
99
16
tan
2
π
9
tan
4
π
11
≈
3.36758
{\displaystyle {\frac {99}{16\tan {\frac {2\pi }{9}}\tan {\frac {4\pi }{11}}}}\approx 3.36758}
Dichoral angles Gishenp–11/4–gishenp: 100° Step–4–gishenp: 90° Step–9/2–step:
3
π
11
≈
49.09091
∘
{\displaystyle {\frac {3\pi }{11}}\approx 49.09091^{\circ }}
Central density 8 Number of external pieces 40 Level of complexity 24 Related polytopes Army Semi-uniform ehendip Dual Enneagrammic-great 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-grand hendecagrammic duoprism , Great enneagrammic-hendecagonal duoprism , Great enneagrammic-small hendecagrammic 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 enneagrammic-great hendecagrammic duoprism , also known as the 9/2-11/4 duoprism , is a uniform duoprism that consists of 11 enneagrammic prisms and 9 great hendecagrammic prisms , with 2 of each at each vertex.
The name can also refer to the great enneagrammic-great hendecagrammic duoprism .
The vertex coordinates of an enneagrammic-great hendecagrammic duoprism, centered at the origin and with edge length 4sin(2π/9)sin(4π/11), are given by:
(
2
sin
4
π
11
,
0
,
2
sin
2
π
9
,
0
)
{\displaystyle \left(2\sin {\frac {4\pi }{11}},\,0,\,2\sin {\frac {2\pi }{9}},\,0\right)}
(
2
sin
4
π
11
,
0
,
2
sin
2
π
9
cos
(
k
π
11
)
,
±
2
sin
2
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {4\pi }{11}},\,0,\,2\sin {\frac {2\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
(
2
sin
4
π
11
cos
(
j
π
9
)
,
±
2
sin
4
π
11
sin
(
j
π
9
)
,
2
sin
2
π
9
,
0
)
{\displaystyle \left(2\sin {\frac {4\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\,\pm 2\sin {\frac {4\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),\,2\sin {\frac {2\pi }{9}},\,0\right)}
(
2
sin
4
π
11
cos
(
j
π
9
)
,
±
2
sin
4
π
11
sin
(
j
π
9
)
,
2
sin
2
π
9
cos
(
k
π
11
)
,
±
2
sin
2
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {4\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\,\pm 2\sin {\frac {4\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),\,2\sin {\frac {2\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
(
−
sin
4
π
11
,
±
3
sin
4
π
11
,
2
sin
2
π
9
,
0
)
{\displaystyle \left(-\sin {\frac {4\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {4\pi }{11}},\,2\sin {\frac {2\pi }{9}},\,0\right)}
(
−
sin
4
π
11
,
±
3
sin
4
π
11
,
2
sin
2
π
9
cos
(
k
π
11
)
,
±
2
sin
2
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(-\sin {\frac {4\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {4\pi }{11}},\,2\sin {\frac {2\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
where j = 2, 4, 8 and k = 2, 4, 6, 8, 10.
