Fourth noble pentagonal hecatonicosahedron
The fourth noble pentagonal hecatonicosahedron is a noble polyhedron. Its 120 congruent faces are asymmetric convex pentagons that meet at congruent order5 vertices. It is a faceting of a semiuniform great rhombicosidodecahedral convex hull.
Fourth noble pentagonal hecatonicosahedron  

Rank  3 
Type  Noble 
Elements  
Faces  120 asymmetric convex pentagons 
Edges  60+60+60+120 
Vertices  120 
Vertex figure  Asymmetric pentagram 
Measures (edge lengths ≈0.32925, ≈0.89924, ≈1.02190, ≈1.83437)  
Edge length ratio  ≈5.57136 
Circumradius  1 
Related polytopes  
Army  Semiuniform Grid, edge lengths ≈0.12089 (between rectangle and ditrigon), ≈0.30625 (between rectangle and dipentagon), ≈0.30140 (between ditrigon and dipentagon) 
Dual  Sixth noble kipentagrammic hecatonicosahedron 
Convex core  NonCatalan disdyakis triacontahedron 
Abstract & topological properties  
Flag count  1200 
Euler characteristic  –60 
Orientable  Yes 
Genus  31 
Properties  
Symmetry  H_{3}, order 120 
Flag orbits  10 
Convex  No 
Nature  Tame 
History  
Discovered by  Plasmath 
First discovered  2023 
The ratio between the shortest and longest edges is approximately 1:5.57136.
Gallery edit

The convex hull
Related polyhedra edit
Its convex hull is almost the same as that of the third noble pentagonal hecatonicosahedron.