# Heptagonal duotruncatoprism

The heptagonal duotruncatoprism or hedtep is a convex isogonal polychoron and the sixth member of the duotruncatoprism family. It consists of 14 diheptagonal prisms, 49 rectangular trapezoprisms, 98 wedges, and 49 tetragonal disphenoids. 2 diheptagonal prisms, 2 rectangular trapezoprisms, 3 wedges, and 1 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal heptagonal-diheptagonal duoprisms whose diheptagonal prism cells have a smaller circumradius than their heptagonal prisms. However, it cannot be made uniform.

Heptagonal duotruncatoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymHedtep
Elements
Cells49 tetragonal disphenoids, 98 wedges, 49 rectangular trapezoprisms
Faces196 isosceles triangles, 196 isosceles trapezoids, 98+98 rectangles, 14 diheptagons
Edges98+98+196+196
Vertices196
Vertex figureMirror-symmetric bi-apiculated tetrahedron
Measures (based on tetradecagon edge length 1 and same radius ratio as uniform-derived heptagonal duoexpandoprism)
Edge lengthsEdges of tetradecagons (98+98): 1
Lacing edges (196): ${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {\pi }{14}}}}\approx 3.17771}$
Edges of pseudo-heptagons (196): ${\displaystyle 2(1+\cos {\frac {\pi }{7}})\approx 3.80194}$
Circumradius${\displaystyle {\frac {\sqrt {3+2\cos {\frac {\pi }{7}}}}{2\sin {\frac {\pi }{14}}}}\approx 4.92387}$
Central density1
Related polytopes
ArmyHedtep
RegimentHedtep
DualHeptagonal duotruncatotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
ConvexYes
NatureTame