Fourth noble kipentagrammic hecatonicosahedron

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Fourth noble kipentagrammic hecatonicosahedron
Rank3
TypeNoble
Elements
Faces120 asymmetric pentagrams
Edges60+60+60+120
Vertices120
Vertex figureAsymmetric convex pentagon
Measures (edge lengths ≈1.17048, ≈1.72495, ≈1.92028, ≈1.92802)
Edge length ratio≈1.64720
Circumradius1
Related polytopes
ArmySemi-uniform Grid, edge lengths ≈0.53174 (between rectangle and ditrigon), ≈0.18966 (between rectangle and dipentagon), ≈0.17359 (between ditrigon and dipentagon)
DualFirst noble pentagonal 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 fourth noble kipentagrammic hecatonicosahedron is a noble polyhedron. Its 120 congruent faces are asymmetric pentagrams 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 1:1.64720.

Gallery[edit | edit source]