First noble kisombreroidal hecatonicosahedron

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First noble kisombreroidal hecatonicosahedron
Rank3
TypeNoble
Elements
Faces120 asymmetric pentagons
Edges60+60+60+120
Vertices120
Vertex figureAsymmetric pentagon
Measures (edge lengths ≈0.29174, ≈1.24380, ≈1.85170, ≈1.94016)
Edge length ratio≈6.65031
Circumradius1
Related polytopes
ArmySemi-uniform Grid, edge lengths ≈0.21220 (between rectangle and ditrigon), ≈0.20021 (between rectangle and dipentagon), ≈0.34335 (between ditrigon and dipentagon)
DualSecond 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 kisombreroidal hecatonicosahedron is a noble polyhedron. Its 120 congruent faces are asymmetric 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 1:6.65031.

Gallery[edit | edit source]