Noble pentagrammic tetracontoctahedron
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Noble pentagrammic tetracontoctahedron | |
---|---|
Rank | 3 |
Type | Noble |
Elements | |
Faces | 48 asymmetric pentagrams |
Edges | 24+24+24+48 |
Vertices | 48 |
Vertex figure | Asymmetric pentagon |
Measures (edge lengths 1, ≈1.15859, ≈1.17827, ≈1.22064) | |
Circumradius | ≈0.67039 |
Number of external pieces | 336 |
Level of complexity | 48 |
Related polytopes | |
Army | Semi-uniform Girco, edge lengths ≈0.10972 (between rectangles and ditetragons), ≈0.33839 (between rectangles and ditrigons), ≈0.39959 (between ditrigons and ditetragons) |
Dual | Noble pentagonal tetracontoctahedron |
Convex core | Non-Catalan disdyakis dodecahedron |
Abstract & topological properties | |
Flag count | 480 |
Euler characteristic | –24 |
Schläfli type | {5,5} |
Orientable | Yes |
Genus | 13 |
Properties | |
Symmetry | B3, order 48 |
Convex | No |
Nature | Tame |
History | |
Discovered by | Plasmath |
First discovered | 2023 |
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.