Great hendecagrammic-dodecagonal duoprism

Great hendecagrammic-dodecagonal duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x11/4o x12o ()
Elements
Cells	12 great hendecagrammic prisms, 11 dodecagonal prisms
Faces	132 squares, 12 great hendecagrams, 11 dodecagons
Edges	132+132
Vertices	132
Vertex figure	Digonal disphenoid, edge lengths 2cos(4π/11) (base 1), (√6+√2)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Gishenp–11/4–gishenp: 150°
	Gishenp–4–twip: 90°
	Twip–12–twip:
Central density	4
Number of external pieces	34
Level of complexity	12
Related polytopes
Army	Semi-uniform hentwadip
Dual	Great hendecagrammic-dodecagonal duotegum
Conjugates	Hendecagonal-dodecagonal duoprism, Hendecagonal-dodecagrammic duoprism, Small hendecagrammic-dodecagonal duoprism, Small hendecagrammic-dodecagrammic duoprism, Hendecagrammic-dodecagonal duoprism, Hendecagrammic-dodecagrammic duoprism, Great hendecagrammic-dodecagrammic duoprism, Grand hendecagrammic-dodecagonal duoprism, Grand hendecagrammic-dodecagrammic duoprism
Abstract & topological properties
Flag count	3168
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)×I2(12), order 528
Convex	No
Nature	Tame

The great hendecagrammic-dodecagonal duoprism, also known as the 11/4-12 duoprism, is a uniform duoprism that consists of 12 great hendecagrammic prisms and 11 dodecagonal prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a great hendecagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(4π/11), are given by:

$\left(1,\,0,\,\pm \left(1+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}},\,\pm \left(1+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}}\right)$ ,
$\left(1,\,0,\,\pm \sin {\frac {4\pi }{11}},\,\pm \left(2+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}}\right)$ ,
$\left(1,\,0,\,\pm \left(2+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}},\,\pm \sin {\frac {4\pi }{11}}\right)$ ,
$\left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,\pm \left(1+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}},\,\pm \left(1+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}}\right)$ ,
$\left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,\pm \sin {\frac {4\pi }{11}},\,\pm \left(2+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}}\right)$ ,
$\left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,\pm \left(2+{\sqrt {3}}\right)\sin {\frac {4\pi }{11}},\,\pm \sin {\frac {4\pi }{11}}\right)$ ,