# Enneagonal duotruncatoprism

Enneagonal duotruncatoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymEdtep
Elements
Cells81 tetragonal disphenoids, 162 wedges, 81 rectangular trapezoprisms, 18 dienneagonal prisms
Faces324 isosceles triangles, 324 isosceles trapezoids, 162+162 rectangles, 18 dienneagons
Edges162+162+324+324
Vertices324
Vertex figureMirror-symmetirc bi-apiculated tetrahedron
Measures (based on octadecagon edge length 1 and same radius ratio as uniform-derived enneagonal duoexpandoprism)
Edge lengthsEdges of octadecagons (162+162): 1
Edges of pseudo-enneagons (324): ${\displaystyle 2(1+\cos {\frac {\pi }{9}})\approx 3.87939}$
Lacing edges (324): ${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {\pi }{18}}}}\approx 4.07207}$
Circumradius${\displaystyle {\frac {\sqrt {3+2\cos {\frac {\pi }{9}}}}{2\sin {\frac {\pi }{18}}}}\approx 6.36037}$
Central density1
Related polytopes
ArmyEdtep
RegimentEdtep
DualEnneagonal duotruncatotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(9)≀S2, order 648
ConvexYes
NatureTame

The enneagonal duotruncatoprism or edtep is a convex isogonal polychoron and the eighth member of the duotruncatoprism family. It consists of 18 dienneagonal prisms, 81 rectangular trapezoprisms, 162 wedges, and 81 tetragonal disphenoids. 2 dienneagonal prisms, 2 rectangular trapezoprisms, 3 wedges, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal enneagonal-dienneagonal duoprisms whose dienneagonal prisms have a smaller circumradius than their enneagonal prisms. However, it cannot be made uniform.