Enneagonal antiditetragoltriate

Enneagonal antiditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Eadet
Elements
Cells	81+81 tetragonal disphenoids, 162 rectangular pyramids, 18 enneagonal prisms
Faces	324+324 isosceles triangles, 162 rectangles, 18 enneagons
Edges	162+162+324
Vertices	162
Vertex figure	Biaugmented triangular prism
Measures (based on same duoprisms as optimized enneagonal ditetragoltriate)
Edge lengths	Edges of smaller enneagon (162): 1
	Lacing edges (324): ${\frac {\sqrt {\frac {2+\cos {\frac {\pi }{9}}+{\sqrt {2}}\sin {\frac {\pi }{9}}}{2}}}{\cos {\frac {\pi }{18}}}}\approx 1.32850$
	Edges of larger enneagon (162): $1+{\sqrt {2}}\sin {\frac {\pi }{9}}\approx 1.48369$
Circumradius	${\sqrt {\frac {1+{\frac {\sqrt {2}}{\sin {\frac {\pi }{9}}}}+{\frac {1}{\sin ^{2}{\frac {\pi }{9}}}}}{2}}}\approx 2.61568$
Central density	1
Related polytopes
Army	Eadet
Regiment	Eadet
Dual	Enneagonal antitetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(9)≀S2, order 648
Convex	Yes
Nature	Tame

The enneagonal antiditetragoltriate or eadet is a convex isogonal polychoron and the seventh member of the antiditetragoltriate family. It consists of 18 enneagonal prisms, 162 rectangular pyramids, and 162 tetragonal disphenoids of two kinds. 2 enneagonal prisms, 4 tetragonal disphenoids, and 5 rectanguar 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 enneagonal duoprisms where the larger enneagon is more than ${\frac {1}{\cos {\frac {\pi }{9}}}}$ times the edge length of the smaller one.