Hendecagonal duoexpandoprism

Hendecagonal duoexpandoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Hendep
Coxeter diagram	xo11xx ox11xx&#zy
Elements
Cells	121 tetragonal disphenoids, 242 wedges, 121 rectangular trapezoprisms, 22+22 hendecagonal prisms
Faces	484 isosceles triangles, 484 isosceles trapezoids, 242+242 rectangles, 44 hendecagons
Edges	242+242+484+484
Vertices	484
Vertex figure	Mirror-symmetric triangular antiprism
Measures (based on two hendecagonal-icosidigonal duoprisms of edge length 1)
Edge lengths	Edges of duoprisms (242+242+484): 1
	Lacing edges (484): ${\frac {\sqrt {2}}{2\sin {\frac {\pi }{11}}}}\approx 2.50985$
Circumradius	${\frac {\sqrt {{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}+{\frac {1}{\sin ^{2}{\frac {\pi }{22}}}}}}{2}}\approx 3.93614$
Central density	1
Related polytopes
Army	Hendep
Regiment	Hendep
Dual	Hendecagonal duoexpandotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)≀S2, order 968
Convex	Yes
Nature	Tame

The hendecagonal duoexpandoprism or hendep is a convex isogonal polychoron and the tenth member of the duoexpandoprism family. It consists of 44 hendecagonal prisms of two kinds, 121 rectangular trapezoprisms, 242 wedges, and 121 tetragonal disphenoids. 2 hendecagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal hendecagonal-icosidigonal duoprisms, or more generally hendecagonal-dihendecagonal duoprisms, and a subset of its variations can be obtained by expanding the cells of the hendecagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is $1:{\frac {2}{1+{\tan {\frac {\pi }{22}}}{\sqrt {3+4\cos {\frac {\pi }{11}}}}}}\approx 1:1.45352$.