Polyhedron model showing the icosahedron and one of its 58 stellations, by John L. Hudson, Nottingham, England, United Kingdom, 1986-1987

Stellating a polyhedron means extending elements such as edges or face planes until they meet each other. The new figure is a stellation of the original. It was not until 1938 that all 59 possible stellations of the icosahedron were listed. This is the outermost or ‘final’ stellation: it has 180 faces, 270 edges and 92 vertices. John Hudson made all 59 stellations of the icosahedron in cardboard for the Museum between 1986 and 1987.