Solid geometry

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The complete icosahedron, with irregular faces, was first studied in 1900 by Max Bruckner. He extended the stellation theory beyond regular forms, and identified ten stellations of the icosahedron, including the complete stellation.

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Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces consist of n(n-1) rhombi and whose edges are parallel to the n given lines in sets of 2(n-1). Furthermore, for every pair of the n lines, there is a pair of opposite faces whose sides lie in those directions (Ball and Coxeter 1987, p. 141). A zonohedron is a therefore a polyhedron in which every face is centrally…

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