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it is also called "icosahedron" for a plain term. A non-convex polyhedron version is the great icosahedron, a Kepler–Poinsot polyhedron. Both have icosahedral symmetry.

There are 59 stellations of a regular icosahedron (including the original icosahedron itself) according to Coxeter et al. in The Fifty-Nine Icosahedra. Being stellated

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