Truncated heptagonal duoprism

Truncated heptagonal duoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymTahedip
Elements
Cells49 tetragonal disphenoids, 14 truncated heptagonal prisms
Faces196 isosceles triangles, 49 ditetragons, 14 diheptagons
Edges98+98+196
Vertices196
Vertex figureSphenoid
Measures (variant with tetradecagon edge length 1)
Edge lengthsLacing edges (196): ${\displaystyle {\frac {\sqrt {2}}{2\cos {\frac {\pi }{7}}}}\approx 0.78483}$
Circumradius${\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{14}}}}+{\frac {1}{4\cos ^{2}{\frac {\pi }{7}}\tan ^{2}{\frac {\pi }{14}}}}}}\approx 3.31071}$
Central density1
Related polytopes
ArmyTahedip
RegimentTahedip
DualTetrakis heptagonal duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
ConvexYes
NatureTame

The truncated heptagonal duoprism or tahedip is a convex isogonal polychoron that consists of 14 truncated heptagonal prisms and 49 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated heptagonal prisms join at each vertex. It can be formed by truncating the heptagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform heptagonal-tetradecagonal duoprisms chosen such that the tetradecagonal and heptagonal prisms have the same circumradius. if the tetradecagons of this duoprism have edge length 1, the heptagons have edge length ${\displaystyle 1+{\frac {1}{\cos {\frac {\pi }{7}}}}\approx 2.10992}$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\displaystyle {\frac {2\cos {\frac {\pi }{7}}}{\sqrt {2}}}}$ ≈ 1:1.27416.