Noble pentagrammic tetracontoctahedron

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Noble pentagrammic tetracontoctahedron
Rank3
TypeNoble
Elements
Faces48 asymmetric pentagrams
Edges24+24+24+48
Vertices48
Vertex figureAsymmetric pentagon
Measures (edge lengths 1, ≈1.15859, ≈1.17827, ≈1.22064)
Circumradius≈0.67039
Number of external pieces336
Level of complexity48
Related polytopes
ArmySemi-uniform Girco, edge lengths ≈0.10972 (between rectangles and ditetragons), ≈0.33839 (between rectangles and ditrigons), ≈0.39959 (between ditrigons and ditetragons)
DualNoble pentagonal tetracontoctahedron
Convex coreNon-Catalan disdyakis dodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–24
Schläfli type{5,5}
OrientableYes
Genus13
Properties
SymmetryB3, order 48
ConvexNo
NatureTame
History
Discovered byPlasmath
First discovered2023

The noble pentagrammic tetracontoctahedron is a noble polyhedron. Its 48 congruent faces are convex asymmetric pentagrams meeting at congruent order-5 vertices. It is a faceting of a semi-uniform great rhombicuboctahedral convex hull.

The ratio between the longest and shortest edges is 1:a ≈ 1:1.22064.