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 until they meet each other again. The resulting polyhedron is the new stellated polyhedron. Wiktionary has a definition of: Polygon A polygon (literally many angle, see Wiktionary for the etymology) is a closed planar path composed of a finite number of sequential line segments. ... In mathematics, there are three related meanings of the term polyhedron: in the traditional meaning it is a 3-dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. ... In geometry polytope means, first, the generalization to any dimension of polygon in two dimensions, and polyhedron in three dimensions. ...
For example, the first stellation of the cuboctahedron is the compound of the cube and octahedron.
The first stellation of the icosidodecahedron is the compound of the icosahedron and the dodecahedron.
The third stellation can be seen as a compound of six tetragonal disphenoids, very similar to the rigid compound of 6 tetrahedra; again only a slight change in triangle shape from equilateral is necessary to obtain the stellated rhombic dodecahedron.
Stellation is the process of extending the sides of a polygon, the faces of a polyhedron, and generally the cells of a higher-dimensional polytope, until they meet to form a new figure.
Luke examines the stellations of the rhombic dodecahedron.
Luke, Stellations of the rhombic dodecahedron, The Mathematical Gazette 41 (1957), pp.
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