Noble kicapellogrammic hecatonicosahedron

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Noble kicapellogrammic hecatonicosahedron
Rank3
TypeNoble
Elements
Faces120 asymmetric hexagons
Edges60+60+120+120
Vertices120
Vertex figureAsymmetric hexagon
Measures (edge lengths ≈0.26337, ≈1.70498, ≈1.86350, ≈1.96300)
Edge length ratio≈7.45339
Circumradius1
Related polytopes
ArmySemi-uniform Grid, edge lengths ≈0.21631 (between rectangle and ditrigon), ≈0.15025 (between rectangle and dipentagon), ≈0.38295 (between ditrigon and dipentagon)
DualNoble kicapellogrammic hecatonicosahedron
Convex coreNon-Catalan disdyakis triacontahedron
Abstract & topological properties
Flag count1440
Euler characteristic–120
OrientableYes
Genus61
Properties
SymmetryH3, order 120
Flag orbits12
ConvexNo
NatureTame
History
Discovered byPlasmath
First discovered2023

The noble kicapellogrammic hecatonicosahedron is a self-dual noble polyhedron. Its 120 congruent faces are asymmetric hexagons that meet at congruent order-6 vertices. It is a faceting of a semi-uniform great rhombicosidodecahedral convex hull.

The ratio between the shortest and longest edges is approximately 1:7.45339.

Besides a hexecontagonal stephanoid, it is the only self-dual noble polyhedron with 120 faces.

Gallery[edit | edit source]