Enneagonal-hendecagonal duoprism Rank 4 Type Uniform Notation Bowers style acronym E hen dip Coxeter diagram x9o x11o ( Elements Cells 11 enneagonal prisms , 9 hendecagonal prisms Faces 99 squares , 11 enneagons , 9 hendecagons Edges 99+99 Vertices 99 Vertex figure Digonal disphenoid , edge lengths 2cos(π/9) (base 1), 2cos(π/11) (base 2), and √2 (sides)Measures (edge length 1) Circumradius
1
4
sin
2
π
9
+
1
4
sin
2
π
11
≈
2.29931
{\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{9}}}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}}}\approx 2.29931}
Hypervolume
99
16
tan
π
9
tan
π
11
≈
57.89674
{\displaystyle {\frac {99}{16\tan {\frac {\pi }{9}}\tan {\frac {\pi }{11}}}}\approx 57.89674}
Dichoral angles Ep–9–ep:
9
π
11
≈
147.27273
∘
{\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}
Henp–11–henp: 140° Ep–4–henp: 90° Central density 1 Number of external pieces 20 Level of complexity 6 Related polytopes Army Ehendip Regiment Ehendip Dual Enneagonal-hendecagonal duotegum Conjugates 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-small hendecagrammic duoprism , Great enneagrammic-hendecagrammic duoprism , Great enneagrammic-great hendecagrammic duoprism , Great enneagrammic-grand hendecagrammic duoprism Abstract & topological properties Euler characteristic 0 Orientable Yes Properties Symmetry I2 (9)×I2 (11) , order 396Convex Yes Nature Tame
The enneagonal-hendecagonal duoprism or ehendip , also known as the 9-11 duoprism , is a uniform duoprism that consists of 9 hendecagonal prisms and 11 enneagonal prisms , with two of each joining at each vertex.
The coordinates of an enneagonal-hendecagonal duoprism, centered at the origin and with edge length 4sin(π/9)sin(π/11), are given by:
(
2
sin
π
11
,
0
,
2
sin
π
9
,
0
)
{\displaystyle \left(2\sin {\frac {\pi }{11}},0,2\sin {\frac {\pi }{9}},0\right)}
(
2
sin
π
11
,
0
,
2
sin
π
9
cos
(
k
π
11
)
,
±
2
sin
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {\pi }{11}},0,2\sin {\frac {\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\pm 2\sin {\frac {\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
(
2
sin
π
11
cos
(
j
π
9
)
,
±
2
sin
π
11
sin
(
j
π
9
)
,
2
sin
π
9
,
0
)
{\displaystyle \left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),2\sin {\frac {\pi }{9}},0\right)}
(
2
sin
π
11
cos
(
j
π
9
)
,
±
2
sin
π
11
sin
(
j
π
9
)
,
2
sin
π
9
cos
(
k
π
11
)
,
±
2
sin
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),2\sin {\frac {\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\pm 2\sin {\frac {\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
(
−
sin
π
11
,
±
3
sin
π
11
,
2
sin
π
9
,
0
)
{\displaystyle \left(-\sin {\frac {\pi }{11}},\pm {\sqrt {3}}\sin {\frac {\pi }{11}},2\sin {\frac {\pi }{9}},0\right)}
(
−
sin
π
11
,
±
3
sin
π
11
,
2
sin
π
9
cos
(
k
π
11
)
,
±
2
sin
π
9
sin
(
k
π
11
)
)
{\displaystyle \left(-\sin {\frac {\pi }{11}},\pm {\sqrt {3}}\sin {\frac {\pi }{11}},2\sin {\frac {\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\pm 2\sin {\frac {\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)}
where j = 2, 4, 8 and k = 2, 4, 6, 8, 10.
