Hendecagrammic-great hendecagrammic duoprism Rank 4 Type Uniform Notation Coxeter diagram x11/3o x11/4o ( Elements Cells 11 hendecagrammic prisms , 11 great hendecagrammic prisms Faces 121 squares , 11 hendecagrams , 11 great hendecagrams Edges 121+121 Vertices 121 Vertex figure Digonal disphenoid , edge lengths 2cos(3π/11) (base 1), 2cos(4π/11) (base 2), √2 (sides)Measures (edge length 1) Circumradius
1
4
sin
2
3
π
11
+
1
4
sin
2
4
π
11
≈
0.86014
{\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {3\pi }{11}}}}+{\frac {1}{4\sin ^{2}{\frac {4\pi }{11}}}}}}\approx 0.86014}
Hypervolume
121
16
tan
3
π
11
tan
4
π
11
≈
2.99263
{\displaystyle {\frac {121}{16\tan {\frac {3\pi }{11}}\tan {\frac {4\pi }{11}}}}\approx 2.99263}
Dichoral angles Shenp–4–gishenp: 90° Gishenp–11/4–gishenp:
5
π
11
≈
81.81818
∘
{\displaystyle {\frac {5\pi }{11}}\approx 81.81818^{\circ }}
Shenp–11/3–shenp:
3
π
11
≈
49.09091
∘
{\displaystyle {\frac {3\pi }{11}}\approx 49.09091^{\circ }}
Central density 12 Number of external pieces 44 Level of complexity 24 Related polytopes Army Semi-uniform handip Dual Hendecagrammic-great 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 , Small hendecagrammic-grand hendecagrammic duoprism , Hendecagrammic-grand hendecagrammic duoprism , Great hendecagrammic-grand hendecagrammic duoprism Abstract & topological properties Flag count2904 Euler characteristic 0 Orientable Yes Properties Symmetry I2 (11)×I2 (11) , order 484Convex No Nature Tame
The hendecagrammic-great hendecagrammic duoprism , also known as the 11/3-11/4 duoprism , is a uniform duoprism that consists of 11 hendecagrammic prisms and 11 great hendecagrammic prisms , with 2 of each at each vertex.
The name can also refer to the small hendecagrammic-great hendecagrammic duoprism , the great hendecagrammic duoprism , or the great hendecagrammic-grand hendecagrammic duoprism .
The vertex coordinates of a hendecagrammic-great hendecagrammic duoprism, centered at the origin and with edge length 4sin(3π/11)sin(4π/11), are given by:
(
2
sin
4
π
11
,
0
,
2
sin
3
π
11
,
0
)
{\displaystyle \left(2\sin {\frac {4\pi }{11}},\,0,\,2\sin {\frac {3\pi }{11}},\,0\right)}
(
2
sin
4
π
11
,
0
,
2
sin
3
π
11
cos
(
k
π
11
)
,
±
2
sin
3
π
11
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {4\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)}
(
2
sin
4
π
11
cos
(
j
π
11
)
,
±
2
sin
4
π
11
sin
(
j
π
11
)
,
2
sin
3
π
11
,
0
)
{\displaystyle \left(2\sin {\frac {4\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {4\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {3\pi }{11}},\,0\right)}
(
2
sin
4
π
11
cos
(
j
π
11
)
,
±
2
sin
4
π
11
sin
(
j
π
11
)
,
2
sin
3
π
11
cos
(
k
π
11
)
,
±
2
sin
3
π
11
sin
(
k
π
11
)
)
{\displaystyle \left(2\sin {\frac {4\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {4\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.
