The dodecahedron group

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

These objects can be generated by running script inst/dodecahedron.Rmd, which includes some further discussion and technical documentation and creates file dodecahedron.rda which resides (under version control) in the data/ directory.

Examples

permprod(dodecahedron_face)
#> [1] (1,9,3,6,8)(4,10,7,5,12)
#> [coerced from word form]