Pentagonal antiditetragoltriate

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Pentagonal antiditetragoltriate
Rank4
TypeIsogonal
Notation
Bowers style acronymPaddet
Elements
Cells25+25 tetragonal disphenoids, 50 rectangular pyramids, 10 pentagonal prisms
Faces100+100 isosceles triangles, 50 rectangles, 10 pentagons
Edges50+50+100
Vertices50
Vertex figureBiaugmented triangular prism
Measures (based on same duoprisms as optimized pentagonal ditetragoltriate)
Edge lengthsEdges of smaller pentagon (50): 1
 Lacing edges (50):
 Edges of larger pentagon (50):
Circumradius
Central density1
Related polytopes
ArmyPaddet
RegimentPaddet
DualPentagonal antitetrambitriate
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2≀S2, order 200
ConvexYes
NatureTame

The pentagonal antiditetragoltriate or paddet is a convex isogonal polychoron and the third member of the antiditetragoltriate family. It consists of 10 pentagonal prisms, 50 rectangular pyramids, and 50 tetragonal disphenoids of two kinds. 2 pentagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform pentagonal duoprisms where the larger pentagon is more than times the edge length of the smaller one.

The grand antiprism can be thought of as the convex hull of two inversely oriented pentagonal antiditetragoltriates, with the pentagons having a ratio of 1: ≈ 1:1.61803.