# Rectified heptagonal duoprism

Rectified heptagonal duoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymRehedip
Elements
Cells49 tetragonal disphenoids, 14 rectified heptagonal prisms
Faces196 isosceles triangles, 49 squares, 14 heptagons
Edges98+196
Vertices98
Vertex figureWedge
Measures (based on heptagons of edge length 1)
Edge lengthsLacing edges (196): ${\displaystyle {\frac {\sqrt {2}}{2\cos {\frac {\pi }{7}}}}\approx 0.78483}$
Edges of heptagons (98): 1
Circumradius${\displaystyle {\sqrt {{\frac {1}{\sin ^{2}{\frac {2\pi }{7}}}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{7}}}}}}\approx 1.72161}$
Central density1
Related polytopes
ArmyRehedip
RegimentRehedip
DualJoined heptagonal duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
ConvexYes
NatureTame

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 ${\displaystyle {\frac {1}{\cos {\frac {\pi }{7}}}}\approx 1.10992}$ times as long as the edges of the other.

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