Rectified pentagonal duoprism

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Rectified pentagonal duoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymRepdip
Elements
Cells25 tetragonal disphenoids, 10 rectified pentagonal prisms
Faces100 isosceles triangles, 25 squares, 10 pentagons
Edges50+100
Vertices50
Vertex figureWedge
Measures (based on pentagons of edge length 1)
Edge lengthsLacing edges (100):
 Edges of pentagons (50): 1
Circumradius
Central density1
Related polytopes
ArmyRepdip
RegimentRepdip
DualJoined pentagonal duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2≀S2, order 200
ConvexYes
NatureTame

The rectified pentagonal duoprism or repdip is a convex isogonal polychoron that consists of 10 rectified pentagonal prisms and 25 tetragonal disphenoids. 3 rectified pentagonal prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the pentagonal duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform pentagonal duoprisms, where the edges of one pentagon are times as long as the edges of the other.

The ratio between the longest and shortest edges is 1: ≈ 1:1.14412.

Vertex coordinates[edit | edit source]

The vertices of a rectified pentagonal duoprism with pentagons of edge length 1, centered at the origin, are given by: