Heptagonal duotruncatoprism

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

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.