A098112 Number of different colorings of the platonic solids allowing rotation symmetry.

5, 10, 23, 96, 17824

Offset

1,1

Comments

Two colorings of a platonic solid are said to be the same if one is able to pick up the solid and rotate it in such a way as to align the colors.

Links

Table of n, a(n) for n=1..5.

Prog

(Magma) // Tetraeder S4 := SymmetricGroup( 4 ); r := S4 ! (2, 3, 4); s := S4 ! (1, 2)(3, 4); tetraeder := sub< S4 | r, s >; // Hexaeder S6 := SymmetricGroup( 6 ); r := S6 ! (2, 3, 4, 5); s := S6 ! (1, 3, 4)(2, 6, 5); hexaeder := sub< S6 | r, s >; // Octaeder S8 := SymmetricGroup( 8 ); r := S8 ! (1, 2, 3, 4)(5, 6, 7, 8); s := S8 ! (1, 2, 6, 5)(3, 7, 8, 4); octaeder := sub< S8 | r, s >; // Dodecaeder S12 := SymmetricGroup( 12 ); r := S12 ! (2, 3, 4, 5, 6)(7, 8, 9, 10, 11); s := S12 ! (1, 3, 7, 11, 6)(4, 8, 12, 10, 5); dodecaeder := sub< S12 | r, s >; // Icosaeder S20 := SymmetricGroup( 20 ); r := S20 ! (1, 2, 3, 4, 5)(6, 8, 10, 12, 14)(7, 9, 11, 13, 15)(16, 17, 18, 19, 20); s := S20 ! (1, 2, 8, 7, 6)(3, 9, 16, 15, 5)(10, 17, 20, 14, 4)(11, 18, 19, 13, 12); icosaeder := sub< S20 | r, s >; for G in [tetraeder, hexaeder, octaeder, dodecaeder, icosaeder] do &+[ c[2] * n^( &+[ t[2]: t in CycleStructure( c[3] ) ] ): c in C ] / #G; end for;

Crossrefs

Sequence in context: A175661 A355552 A197174 * A237435 A280721 A300552

Adjacent sequences: A098109 A098110 A098111 * A098113 A098114 A098115

Keyword

nonn,fini,full

Author

Daan Wanrooy (wanrooy(AT)math.ru.nl), Sep 24 2004

Status

approved