Stellation
From Free net encyclopedia
Stellation is a process of constructing new polygons (in two dimensions), new polyhedra in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes in a symmetrical way until they meet each other again.
Stellation of a regular polygon forms a star polygon or polygon compound. Stellation of a pentagon, for instance, forms a pentagram.
Of the Platonic solids, three can be stellated and two cannot. The face-planes of the tetrahedron and cube meet only at the edges of the original polyhedra, so there are no stellations. The regular octahedron has one stellation, the stella octangula.
The dodecahedron has three stellations, the small stellated dodecahedron, the great dodecahedron, and the great stellated dodecahedron.
Stellation of the icosahedron is complicated compared to the other Platonic solids. The number of possible forms depends upon what counts as a stellation. Using a set of rules proposed by J.C.P. Miller, there are 58 stellations, including such figures as the triakis icosahedron, the compound of five octahedra, the great icosahedron, the compound of five tetrahedra, and the compound of ten tetrahedra.
See also
- List of Wenninger polyhedron models Includes 44 stellated forms of the octahedron, dodecahedron, icosahedron, and icosidodecahedron, enumerated the 1974 book "Polyhedron Models" by Magnus Wenninger
- Polyhedral compound Includes 5 regular compounds and 4 dual regular compounds.
Template:Geometry-stubja:星型多面体 pt:Estrelamento de um poliedro