# Enneagonal ditetragoltriate

Enneagonal ditetragoltriate
Rank4
TypeIsogonal
Notation
Bowers style acronymEdet
Elements
Cells81 rectangular trapezoprisms, 18 enneagonal prisms
Faces162 isosceles trapezoids, 162 rectangles, 18 enneagons
Edges81+162+162
Vertices162
Vertex figureNotch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengthsEdges of smaller enneagon (162): 1
Lacing edges (81): 1
Edges of larger enneagon (162): ${\displaystyle 1+{\sqrt {2}}\sin {\frac {\pi }{9}}\approx 1.48369}$
Circumradius${\displaystyle {\sqrt {\frac {1+{\frac {\sqrt {2}}{\sin {\frac {\pi }{9}}}}+{\frac {1}{\sin ^{2}{\frac {\pi }{9}}}}}{2}}}\approx 2.61568}$
Central density1
Related polytopes
ArmyEdet
RegimentEdet
DualEnneagonal tetrambitriate
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(9)≀S2, order 648
ConvexYes
NatureTame

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:${\displaystyle 1+{\sin {\frac {\pi }{9}}}{\sqrt {2}}}$ ≈ 1:1.48369. This value is also the ratio between the two sides of the two semi-uniform duoprisms.