# Hendecagonal duoexpandoprism

Hendecagonal duoexpandoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymHendep
Coxeter diagramxo11xx ox11xx&#zy
Elements
Cells121 tetragonal disphenoids, 242 wedges, 121 rectangular trapezoprisms, 22+22 hendecagonal prisms
Faces484 isosceles triangles, 484 isosceles trapezoids, 242+242 rectangles, 44 hendecagons
Edges242+242+484+484
Vertices484
Vertex figureMirror-symmetric triangular antiprism
Measures (based on two hendecagonal-icosidigonal duoprisms of edge length 1)
Edge lengthsEdges of duoprisms (242+242+484): 1
Lacing edges (484): ${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {\pi }{11}}}}\approx 2.50985}$
Circumradius${\displaystyle {\frac {\sqrt {{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}+{\frac {1}{\sin ^{2}{\frac {\pi }{22}}}}}}{2}}\approx 3.93614}$
Central density1
Related polytopes
ArmyHendep
RegimentHendep
DualHendecagonal duoexpandotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
ConvexYes
NatureTame

The hendecagonal duoexpandoprism or hendep is a convex isogonal polychoron and the tenth member of the duoexpandoprism family. It consists of 44 hendecagonal prisms of two kinds, 121 rectangular trapezoprisms, 242 wedges, and 121 tetragonal disphenoids. 2 hendecagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal hendecagonal-icosidigonal duoprisms, or more generally hendecagonal-dihendecagonal duoprisms, and a subset of its variations can be obtained by expanding the cells of the hendecagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is ${\displaystyle 1:{\frac {2}{1+{\tan {\frac {\pi }{22}}}{\sqrt {3+4\cos {\frac {\pi }{11}}}}}}\approx 1:1.45352}$.