Rectified heptagonal duoprism

Rectified heptagonal duoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Rehedip
Elements
Cells	49 tetragonal disphenoids, 14 rectified heptagonal prisms
Faces	196 isosceles triangles, 49 squares, 14 heptagons
Edges	98+196
Vertices	98
Vertex figure	Wedge
Measures (based on heptagons of edge length 1)
Edge lengths	Lacing edges (196): ${\frac {\sqrt {2}}{2\cos {\frac {\pi }{7}}}}\approx 0.78483$
	Edges of heptagons (98): 1
Circumradius	${\sqrt {{\frac {1}{\sin ^{2}{\frac {2\pi }{7}}}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{7}}}}}}\approx 1.72161$
Central density	1
Related polytopes
Army	Rehedip
Regiment	Rehedip
Dual	Joined heptagonal duotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)≀S2, order 392
Convex	Yes
Nature	Tame

The rectified heptagonal duoprism or rehedip is a convex isogonal polychoron that consists of 14 rectified heptagonal prisms and 49 tetragonal disphenoids. 3 rectified heptagonal prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the heptagonal duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform heptagonal duoprisms, where the edges of one heptagon are ${\frac {1}{\cos {\frac {\pi }{7}}}}\approx 1.10992$ times as long as the edges of the other.

The ratio between the longest and shortest edges is 1:${\frac {2\cos {\frac {\pi }{7}}}{\sqrt {2}}}$ ≈ 1:1.27416.