Fourth noble pentagonal hecatonicosahedron

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Fourth noble pentagonal hecatonicosahedron
Rank3
TypeNoble
Elements
Faces120 asymmetric convex pentagons
Edges60+60+60+120
Vertices120
Vertex figureAsymmetric pentagram
Measures (edge lengths ≈0.32925, ≈0.89924, ≈1.02190, ≈1.83437)
Edge length ratio≈5.57136
Circumradius1
Related polytopes
ArmySemi-uniform Grid, edge lengths ≈0.12089 (between rectangle and ditrigon), ≈0.30625 (between rectangle and dipentagon), ≈0.30140 (between ditrigon and dipentagon)
DualSixth 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 fourth 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 1:5.57136.

Gallery[edit | edit source]

Related polyhedra[edit | edit source]

Its convex hull is almost the same as that of the third noble pentagonal hecatonicosahedron.