Enneagonal ditetragoltriate

Enneagonal ditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Edet
Elements
Cells	81 rectangular trapezoprisms, 18 enneagonal prisms
Faces	162 isosceles trapezoids, 162 rectangles, 18 enneagons
Edges	81+162+162
Vertices	162
Vertex figure	Notch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengths	Edges of smaller enneagon (162): 1
	Lacing edges (81): 1
	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	Edet
Regiment	Edet
Dual	Enneagonal tetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(9)≀S2, order 648
Convex	Yes
Nature	Tame

The enneagonal ditetragoltriate or edet is a convex isogonal polychoron and the seventh member of the ditetragoltriate family. It consists of 18 enneagonal prisms and 81 rectangular trapezoprisms. 2 enneagonal prisms and 4 rectangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal enneagonal prismatic swirlchora.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$1+{\sin {\frac {\pi }{9}}}{\sqrt {2}}$ ≈ 1:1.48369. This value is also the ratio between the two sides of the two semi-uniform duoprisms.