First noble pentagonal hecatonicosahedron

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First noble pentagonal hecatonicosahedron
Rank3
TypeNoble
Elements
Faces120 asymmetric convex pentagons
Edges60+60+60+120
Vertices120
Vertex figureAsymmetric pentagram
Measures (edge lengths ≈0.06535, ≈0.62055, ≈1.70215, ≈1.88956)
Edge length ratio≈28.91446
Circumradius1
Related polytopes
ArmySemi-uniform Grid, edge lengths ≈0.06530 (between rectangle and ditrigon), ≈0.00643 (between rectangle and dipentagon), ≈0.57999 (between ditrigon and dipentagon)
DualFourth noble kipentagrammic hecatonicosahedron
Convex coreNon-Catalan disdyakis triacontahedron
Abstract & topological properties
Flag count1200
Euler characteristic–60
OrientableYes
Genus31
Properties
SymmetryH3, order 120\
Flag orbits10
ConvexNo
NatureTame
History
Discovered byPlasmath
First discovered2023

The first noble pentagonal hecatonicosahedron is a noble polyhedron. Its 120 congruent faces are asymmetric convex pentagons that meet at congruent order-5 vertices. It is a faceting of a semi-uniform great rhombicosidodecahedral convex hull.

The ratio between the shortest and longest edges is approximately 1:28.91446.

Gallery[edit | edit source]