Tenth noble kipentagrammic hecatonicosahedron

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Tenth noble kipentagrammic hecatonicosahedron
Rank3
TypeNoble
Elements
Faces120 asymmetric pentagrams
Edges60+120+120
Vertices120
Vertex figureAsymmetric pentagon
Measures (edge lengths ≈1.59264, ≈1.75941, ≈1.95741)
Edge length ratio≈1.22903
Circumradius1
Related polytopes
ArmySemi-uniform Grid, edge lengths ≈0.41055 (between rectangle and ditrigon), ≈0.17723 (between rectangle and dipentagon), ≈0.25373 (between ditrigon and dipentagon)
DualFissary noble in tioid 8 army
Convex coreNon-Catalan pentakis dodecahedron
Abstract & topological properties
Flag count1200
Euler characteristic–60
Schläfli type{5,5}
OrientableYes
Genus31
Properties
SymmetryH3, order 120
Flag orbits10
ConvexNo
NatureTame
History
Discovered byPlasmath
First discovered2022

The tenth 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 1:1.22903.

Related polyhedra[edit | edit source]