First noble kipentagrammic hexecontahedron
(Redirected from First kipentagrammic hexecontahedron)
First noble kipentagrammic hexecontahedron | |
---|---|
Rank | 3 |
Type | Noble |
Elements | |
Faces | 60 asymmetric pentagrams |
Edges | 30+60+60 |
Vertices | 60 |
Vertex figure | Asymmetric pentagon |
Measures (edge lengths , , ) | |
Edge length ratio | |
Circumradius | |
Number of external pieces | 600 |
Level of complexity | 72 |
Related polytopes | |
Army | Semi-uniform Ti, edge lengths (pentagons) and (between ditrigons) |
Dual | First kipiscoidal hexecontahedron |
Conjugate | First kipiscoidal hexecontahedron |
Convex core | Deltoidal hexecontahedron |
Abstract & topological properties | |
Flag count | 600 |
Euler characteristic | –30 |
Schläfli type | {5,5} |
Orientable | Yes |
Genus | 16 |
Properties | |
Symmetry | H3+, order 60 |
Flag orbits | 10 |
Convex | No |
Nature | Tame |
The first noble kipentagrammic hexecontahedron is a noble polyhedron. Its 60 congruent faces are asymmetric pentagrams meeting at congruent order-5 vertices. It is a faceting of the same semi-uniform truncated icosahedron hull as that of the truncated great dodecahedron.
The ratio between the shortest and longest edges is 1: ≈ 1:1.37638.
Vertex coordinates[edit | edit source]
The coordinates of a first noble kipentagrammic hexecontahedron are all even permutations of:
- ,
- ,
plus all permutations of
- .
These are the same coordinates as the first noble crossed kignathogrammic hexecontahedron, first noble ditrapezoidal hexecontahedron, fourth kisombreroidal hexecontahedron, and second kisombreroidal hexecontahedron