Hendecagonal ditetragoltriate

Hendecagonal ditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Hendet
Elements
Cells	121 rectangular trapezoprisms, 22 hendecagonal prisms
Faces	242 isosceles trapezoids, 242 rectangles, 22 hendecagons
Edges	121+242+242
Vertices	242
Vertex figure	Notch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengths	Edges of smaller hendecagon (242): 1
	Lacing edges (121): 1
	Edges of larger hendecagon (242): $1+{\sqrt {2}}\sin {\frac {\pi }{11}}\approx 1.39843$
Circumradius	${\sqrt {\frac {1+{\frac {\sqrt {2}}{\sin {\frac {\pi }{11}}}}+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}{2}}}\approx 3.05110$
Central density	1
Related polytopes
Army	Hendet
Regiment	Hendet
Dual	Hendecagonal tetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)≀S2, order 968
Convex	Yes
Nature	Tame

The hendecagonal ditetragoltriate or hendet is a convex isogonal polychoron and the ninth member of the ditetragoltriate family. It consists of 22 hendecagonal prisms and 121 rectangular trapezoprisms. 2 hendecagonal prisms and 4 retangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal hendecagonal prismatic swirlchora.

It can be obtained as the convex hull of 2 similarly oriented semi-uniform hendecagonal duoprisms, one with a larger xy hendecagon and the other with a larger zw hendecagon.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$1+{\sin {\frac {\pi }{11}}}{\sqrt {2}}$ ≈ 1:1.39843. This value is also the ratio between the two sides of the two semi-uniform duoprisms.