Hendecagrammic duoprism

Hendecagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Coxeter diagram	x11/3o x11/3o ()
Elements
Cells	22 hendecagrammic prisms
Faces	121 squares, 22 hendecagrams
Edges	242
Vertices	121
Vertex figure	Tetragonal disphenoid, edge lengths 2cos(3π/11) (bases) and √2 (sides)
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dichoral angles	Shenp–4–shenp: 90°
	Shenp–11/3–shenp:
Central density	9
Number of external pieces	44
Level of complexity	12
Related polytopes
Army	Handip
Dual	Hendecagrammic duotegum
Conjugates	Hendecagonal duoprism, Small hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)≀S2, order 968
Convex	No
Nature	Tame

The hendecagrammic duoprism, also known as the hendecagrammic-hendecagrammic duoprism, the 11/3 duoprism or the 11/3-11/3 duoprism, is a noble uniform duoprism that consists of 22 hendecagrammic prisms, with 4 meeting at each vertex.

The name can also refer to the small hendecagrammic duoprism, the small hendecagrammic-hendecagrammic duoprism, the small hendecagrammic-great hendecagrammic duoprism, the small hendecagrammic-grand hendecagrammic duoprism, the hendecagrammic-great hendecagrammic duoprism, the hendecagrammic-grand hendecagrammic duoprism, the great hendecagrammic duoprism, the great hendecagrammic-grand hendecagrammic duoprism, or the grand hendecagrammic duoprism.

Vertex coordinates[edit | edit source]

The coordinates of a hendecagrammic duoprism, centered at the origin and with edge length 2sin(3π/11), are given by:

$\left(1,\,0,\,1,\,0\right),$
$\left(1,\,0,\,\cos\left(\frac{k\pi}{11}\right),\,±\sin\left(\frac{k\pi}{11}\right)\right),$
$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,1,\,0\right),$
$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,\cos\left(\frac{k\pi}{11}\right),\,±\sin\left(\frac{k\pi}{11}\right)\right),$