Hendecagonal antiditetragoltriate

Hendecagonal antiditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Henadet
Elements
Cells	121+121 tetragonal disphenoids, 242 rectangular pyramids, 22 hendecagonal prisms
Faces	484+484 isosceles triangles, 242 rectangles, 22 hendecagons
Edges	242+242+484
Vertices	242
Vertex figure	Biaugmented triangular prism
Measures (based on same duoprisms as optimized hendecagonal ditetragoltriate)
Edge lengths	Edges of smaller hendecagon (242): 1
	Lacing edges (484): ${\frac {\sqrt {\frac {2+\cos {\frac {\pi }{11}}+{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}}}{\cos {\frac {\pi }{22}}}}\approx 1.30907$
	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	Henadet
Regiment	Henadet
Dual	Hendecagonal antitetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)≀S2, order 968
Convex	Yes
Nature	Tame

The hendecagonal antiditetragoltriate or henadet is a convex isogonal polychoron and the ninth member of the antiditetragoltriate family. It consists of 22 hendecagonal prisms, 242 rectangular pyramids, and 242 tetragonal disphenoids of two kinds. 2 hendecagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform hendecagonal duoprisms where the larger hendecagon is more than ${\frac {1}{\cos {\frac {\pi }{11}}}}$ times the edge length of the smaller one.