# Hendecagonal ditetragoltriate

Hendecagonal ditetragoltriate
Rank4
TypeIsogonal
Notation
Bowers style acronymHendet
Elements
Cells121 rectangular trapezoprisms, 22 hendecagonal prisms
Faces242 isosceles trapezoids, 242 rectangles, 22 hendecagons
Edges121+242+242
Vertices242
Vertex figureNotch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengthsEdges 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 density1
Related polytopes
ArmyHendet
RegimentHendet
DualHendecagonal tetrambitriate
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
ConvexYes
NatureTame

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.