Heptagonal ditetragoltriate

Heptagonal ditetragoltriate
Rank4
TypeIsogonal
Notation
Bowers style acronymHedet
Elements
Cells49 rectangular trapezoprisms, 14 heptagonal prisms
Faces98 isosceles trapezoids, 98 rectangles, 14 heptagons
Edges49+98+98
Vertices98
Vertex figureNotch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengthsEdges of smaller heptagon (98): 1
Lacing edges (49): 1
Edges of larger heptagon (98): ${\displaystyle 1+{\sqrt {2}}\sin {\frac {\pi }{7}}\approx 1.61360}$
Circumradius${\displaystyle {\sqrt {\frac {1+{\frac {\sqrt {2}}{\sin {\frac {\pi }{7}}}}+{\frac {1}{\sin ^{2}{\frac {\pi }{7}}}}}{2}}}\approx 2.18762}$
Central density1
Related polytopes
ArmyHedet
RegimentHedet
DualHeptagonal tetrambitriate
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
ConvexYes
NatureTame

The heptagonal ditetragoltriate or hedet is a convex isogonal polychoron and the fifth member of the ditetragoltriate family. It consists of 14 heptagonal prisms and 49 rectangular trapezoprisms. 2 heptagonal prisms and 4 rectangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal heptagonal prismatic swirlchora.

It can be obtained as the convex hull of 2 similarly oriented semi-uniform heptagonal duoprisms, one with a larger xy heptagon and the other with a larger zw heptagon.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\displaystyle 1+{\sin {\frac {\pi }{7}}}{\sqrt {2}}}$ ≈ 1:1.61360. This value is also the ratio between the two sides of the two semi-uniform duoprisms.