Facetting operation

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A regular icosahedron
A regular great dodecahedron
The great dodecahedron (right) is the second-order facetting, , of the icosahedron.

The facetting operation is an operation which replaces the faces of a polyhedron with its k -holes. If a polyhedron has a triangular vertex figure, then its (second-order) facetting will be itself.

Definition[edit | edit source]

For a regular polyhedron P  with distinguished generators the k -order facetting, , of P  is given by the generators:

The first-order facetting of a polyhedron is itself.

Examples[edit | edit source]