Octagonal-hendecagonal duoprism Rank 4 Type Uniform Notation Bowers style acronym O hen dip Coxeter diagram x8o x11o ( Elements Cells 11 octagonal prisms , 8 hendecagonal prisms Faces 88 squares , 11 octagons , 8 hendecagons Edges 88+88 Vertices 88 Vertex figure Digonal disphenoid , edge lengths √2+√2 (base 1), 2cos(π/11) (base 2), and √2 (sides)Measures (edge length 1) Circumradius
2
+
2
2
+
1
4
sin
2
π
11
≈
2.20381
{\displaystyle {\sqrt {{\frac {2+{\sqrt {2}}}{2}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}}}\approx 2.20381}
Hypervolume
11
(
1
+
2
)
2
tan
π
11
≈
45.22131
{\displaystyle {\frac {11(1+{\sqrt {2}})}{2\tan {\frac {\pi }{11}}}}\approx 45.22131}
Dichoral angles Op–8–op:
9
π
11
≈
147.27273
∘
{\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}
Henp–11–henp: 135° Op–4–henp: 90° Central density 1 Number of external pieces 19 Level of complexity 6 Related polytopes Army Ohendip Regiment Ohendip Dual Octagonal-hendecagonal duotegum Conjugates Octagonal-small hendecagrammic duoprism , Octagonal-hendecagrammic duoprism , Octagonal-great hendecagrammic duoprism , Octagonal-grand hendecagrammic duoprism , Octagrammic-hendecagonal duoprism , Octagrammic-small hendecagrammic duoprism , Octagrammic-hendecagrammic duoprism , Octagrammic-great hendecagrammic duoprism , Octagrammic-grand hendecagrammic duoprism Abstract & topological properties Flag count2112 Euler characteristic 0 Orientable Yes Properties Symmetry I2 (8)×I2 (11) , order 352Flag orbits 6 Convex Yes Nature Tame
The octagonal-hendecagonal duoprism or ohendip , also known as the 8-11 duoprism , is a uniform duoprism that consists of 8 hendecagonal prisms and 11 octagonal prisms , with two of each joining at each vertex.
The coordinates of an octagonal-hendecagonal duoprism, centered at the origin and with edge length 2sin(π/11), are given by:
(
±
sin
π
11
,
±
(
1
+
2
)
sin
π
11
,
1
,
0
)
{\displaystyle \left(\pm \sin {\frac {\pi }{11}},\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},1,0\right)}
(
±
sin
π
11
,
±
(
1
+
2
)
sin
π
11
,
cos
(
j
π
11
)
,
±
sin
(
j
π
11
)
)
{\displaystyle \left(\pm \sin {\frac {\pi }{11}},\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\cos \left({\frac {j\pi }{11}}\right),\pm \sin \left({\frac {j\pi }{11}}\right)\right)}
(
±
(
1
+
2
)
sin
π
11
,
±
sin
π
11
,
1
,
0
)
{\displaystyle \left(\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\pm \sin {\frac {\pi }{11}},1,0\right)}
(
±
(
1
+
2
)
sin
π
11
,
±
sin
π
11
,
cos
(
j
π
11
)
,
±
sin
(
j
π
11
)
)
{\displaystyle \left(\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\pm \sin {\frac {\pi }{11}},\cos \left({\frac {j\pi }{11}}\right),\pm \sin \left({\frac {j\pi }{11}}\right)\right)}
where j = 2, 4, 6, 8, 10.
An octagonal-hendecagonal duoprism has the following Coxeter diagrams :
x8o x11o ( (full symmetry)
x4x x11o ( (B2 ×I2 (11) symmetry, octagons as ditetragons) 
