dodecahedron: The dodecahedron group

In permutations: The Symmetric Group: Permutations of a Finite Set

The dodecahedron group

Description

Permutations comprising the dodecahedron group on either its faces or its edges; also the full dodecahedron group

Details

The package provides a number of objects for investigating dodecahedral groups:

Object dodecahedron_face is a cycle object with 60 elements corresponding to the permutations of the faces of a dodecahedron, numbered 1-12 as in the megaminx net. Object dodecahedron_edge is the corresponding object for permuting the edges of a dodecahedron. The edges are indexed by the lower of the two adjoining facets on the megaminx net.

Objects full_dodecahedron_face and full_dodecahedron_edge give the 120 elements of the full dodecahedron group, that is, the dodecahedron group including reflections. NB: these objects are not isomorphic to S5.

Note

File zzz_dodecahedron.R is not really intended to be human-readable. The source file is in inst/dodecahedron_group.py and inst/full_dodecahedron_group.py which contain documented python source code.

Examples

permprod(dodecahedron_face)

permutations documentation built on April 3, 2025, 7:09 p.m.