Rectified dodecagonal duoprism

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Rectified dodecagonal duoprism
Rectified 12 duoprism.png
Rank4
TypeIsogonal
SpaceSpherical
Notation
Bowers style acronymRetwadip
Elements
Cells144 tetragonal disphenoids, 24 rectified dodecagonal prisms
Faces576 isosceles triangles, 144 squares, 24 dodecagons
Edges288+576
Vertices288
Vertex figureWedge
Measures (based on dodecagons of edge length 1)
Edge lengthsLacing edges (576):
 Edges of dodecagons (288): 1
Circumradius
Central density1
Related polytopes
ArmyRetwadip
RegimentRetwadip
DualJoined dodecagonal duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12)≀S2, order 1152
ConvexYes
NatureTame

The rectified dodecagonal duoprism or retwadip is a convex isogonal polychoron that consists of 24 rectified dodecagonal prisms and 144 tetragonal disphenoids. 3 rectified dodecagonal prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the dodecagonal duoprism.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.36603.

Vertex coordinates[edit | edit source]

The vertices of a rectified dodecagonal duoprism based on dodecagons of edge length 1, centered at the origin, are given by: