Truncated heptagonal duoprism

Truncated heptagonal duoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Tahedip
Elements
Cells	49 tetragonal disphenoids, 14 truncated heptagonal prisms
Faces	196 isosceles triangles, 49 ditetragons, 14 diheptagons
Edges	98+98+196
Vertices	196
Vertex figure	Sphenoid
Measures (variant with tetradecagon edge length 1)
Edge lengths	Lacing edges (196): ${\frac {\sqrt {2}}{2\cos {\frac {\pi }{7}}}}\approx 0.78483$
	Edges of tetradecagons (98+98): 1
Circumradius	${\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{14}}}}+{\frac {1}{4\cos ^{2}{\frac {\pi }{7}}\tan ^{2}{\frac {\pi }{14}}}}}}\approx 3.31071$
Central density	1
Related polytopes
Army	Tahedip
Regiment	Tahedip
Dual	Tetrakis heptagonal duotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)≀S2, order 392
Convex	Yes
Nature	Tame

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 $1+{\frac {1}{\cos {\frac {\pi }{7}}}}\approx 2.10992$.

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