A343433
Sorted numbers of (undirected) Hamiltonian cycles in the graphs of the Archimedean solids.
Original entry on oeis.org
3, 6, 30, 44, 100, 1090, 1342, 6020, 39040, 845340, 47629064, 1446402032, 288087704535697
Offset: 1
The solids are in order:
truncated tetrahedron (3),
truncated cube (6),
truncated dodecahedron (30),
truncated octahedron (44),
cuboctahedron (100),
truncated icosahedron (1090),
truncated cuboctahedron (1342),
rhombicuboctahedron (6020),
icosidodecahedron (39040),
snub cube (845340),
truncated icosidodecahedron (47629064),
rhombicosidodecahedron (1446402032),
snub dodecahedron (288087704535697).
A343434
Sorted numbers of (undirected) Hamiltonian cycles in the graphs of the Catalan solids (the Archimedean duals).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 6, 726, 1704, 348912, 1919220, 1685220540, 310880892720
Offset: 1
Six of the Catalan solids are not Hamiltonian, so a(n) = 0 for n <= 6. These solids are: the rhombic dodecahedron, the triakis octahedron, the deltoidal icositetrahedron, the rhombic triacontahedron, the triakis icosahedron, and the deltoidal hexecontahedron.
The remaining (Hamiltonian) solids are in order:
triakis tetrahedron (6),
pentagonal icositetrahedron (726),
tetrakis hexahedron (1704),
disdyakis dodecahedron (348912),
pentagonal hexecontahedron (1919220),
pentakis dodecahedron (1685220540),
disdyakis triacontahedron (310880892720).
Showing 1-2 of 2 results.