Hexagonalhendecagonal duoprismatic prism 


Rank  5 

Type  Uniform 

Notation 

Bowers style acronym  Hahenip 

Coxeter diagram  x x6o x11o () 

Elements 

Tera  11 squarehexagonal duoprisms, 6 squarehendecagonal duoprisms, 2 hexagonalhendecagonal duoprisms 

Cells  66 cubes, 6+12 hendecagonal prisms, 11+22 hexagonal prisms 

Faces  66+66+132 squares, 22 hexagons, 12 hendecagons 

Edges  66+132+132 

Vertices  132 

Vertex figure  Digonal disphenoidal pyramid, edge lengths √3 (disphenoid base 1), 2cos(π/11) (disphenoid base 2), √2 (remaining edges) 

Measures (edge length 1) 

Circumradius  ${\frac {\sqrt {5+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.09754$ 

Hypervolume  ${\frac {33{\sqrt {3}}}{8\tan {\frac {\pi }{11}}}}\approx 24.33265$ 

Diteral angles  Shiddip–hip–shiddip: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$ 

 Shendip–henp–shendip: 120° 

 Shendip–cube–shiddip: 90° 

 Hahendip–hip–shiddip: 90° 

 Shendip–henp–hahendip: 90° 

Height  1 

Central density  1 

Number of external pieces  19 

Level of complexity  30 

Related polytopes 

Army  Hahenip 

Regiment  Hahenip 

Dual  Hexagonalhendecagonal duotegmatic tegum 

Conjugates  Hexagonalsmall hendecagrammic duoprismatic prism, Hexagonalhendecagrammic duoprismatic prism, Hexagonalgreat hendecagrammic duoprismatic prism, Hexagonalgrand hendecagrammic duoprismatic prism 

Abstract & topological properties 

Euler characteristic  2 

Orientable  Yes 

Properties 

Symmetry  G_{2}×I_{2}(11)×A_{1}, order 528 

Convex  Yes 

Nature  Tame 

The hexagonalhendecagonal duoprismatic prism (OBSA: hahenip) also known as the hexagonalhendecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 hexagonalhendecagonal duoprisms, 6 squarehendecagonal duoprisms, and 11 squarehexagonal duoprisms. Each vertex joins 2 squarehexagonal duoprisms, 2 squarehendecagonal duoprisms, and 1 hexagonalhendecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
The vertices of a hexagonalhendecagonal duoprismatic prism of edge length $2\sin(\pi /11)$ are given by:
 $\left(0,\,\pm 2\sin {\frac {\pi }{11}},\,1,\,0,\,\pm \sin {\frac {\pi }{11}}\right)$,
 $\left(\pm {\sqrt {3}}\sin {\frac {\pi }{11}},\,\pm \sin {\frac {\pi }{11}},\,1,\,0,\,\pm \sin {\frac {\pi }{11}}\right)$,
 $\left(0,\,\pm 2\sin {\frac {\pi }{11}},\,\cos {\frac {j\pi }{11}},\,\pm \sin {\frac {j\pi }{11}},\,\pm \sin {\frac {\pi }{11}}\right)$,
 $\left(\pm {\sqrt {3}}\sin {\frac {\pi }{11}},\,\pm \sin {\frac {\pi }{11}},\,\cos {\frac {j\pi }{11}},\,\pm \sin {\frac {j\pi }{11}},\,\pm \sin {\frac {\pi }{11}}\right)$,
where j = 2, 4, 6, 8, 10.
A hexagonalhendecagonal duoprismatic prism has the following Coxeter diagrams:
 x x6o x11o () (full symmetry)
 x x3x x11o () (hexagons as ditrigons)
 xx6oo xx11oo&#x (hexagonalhendecagonal duoprism atop hexagonalhendecagonal duoprism)
 xx3xx xx11oo&#x