Hexagonal-hendecagonal duoprism

Hexagonal-hendecagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymHahendip
Coxeter diagramx6o x11o ()
Elements
Cells11 hexagonal prisms, 6 hendecagonal prisms
Faces66 squares, 11 hexagons, 6 hendecagons
Edges66+66
Vertices66
Vertex figureDigonal disphenoid, edge lengths 3 (base 1), 2cos(π/11) (base 2), and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {4+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.03708}$
Hypervolume${\displaystyle {\frac {33{\sqrt {3}}}{8\tan {\frac {\pi }{11}}}}\approx 24.33265}$
Dichoral anglesHip–6–hip: ${\displaystyle {\frac {8\pi }{11}}\approx 147.27273^{\circ }}$
Henp–11–Henp: 120°
Hip–4–henp: 90°
Central density1
Number of external pieces17
Level of complexity6
Related polytopes
ArmyHahendip
RegimentHahendip
DualHexagonal-hendecagonal duotegum
ConjugatesHexagonal-small hendecagrammic duoprism, Hexagonal-hendecagrammic duoprism, Hexagonal-great hendecagrammic duoprism, Hexagonal-grand hendecagrammic duoprism
Abstract & topological properties
Flag count1584
Euler characteristic0
OrientableYes
Properties
SymmetryG2×I2(11), order 264
ConvexYes
NatureTame

The hexagonal-hendecagonal duoprism or hahendip, also known as the 6-11 duoprism, is a uniform duoprism that consists of 6 hendecagonal prisms and 11 hexagonal prisms, with two of each joining at each vertex.

Vertex coordinates

The coordinates of a hexagonal-hendecagonal duoprism, centered at the origin and with edge length 2sin(π/11), are given by:

• ${\displaystyle \left(\pm 2\sin {\frac {\pi }{11}},0,1,0\right)}$,
• ${\displaystyle \left(\pm 2\sin {\frac {\pi }{11}},0,\cos \left({\frac {j\pi }{11}}\right),\pm \sin \left({\frac {j\pi }{11}}\right)\right)}$,
• ${\displaystyle \left(\pm \sin {\frac {\pi }{11}},\pm {\sqrt {3}}\sin {\frac {\pi }{11}},1,0\right)}$,
• ${\displaystyle \left(\pm \sin {\frac {\pi }{11}},\pm {\sqrt {3}}\sin {\frac {\pi }{11}},\cos \left({\frac {j\pi }{11}}\right),\pm \sin \left({\frac {j\pi }{11}}\right)\right)}$,

where j = 2, 4, 6, 8, 10.

Representations

A hexagonal-hendecagonal duoprism has the following Coxeter diagrams:

• x6o x11o () (full symmetry)
• x3x x11o () (hexagons as ditrigons)