About: Eberhard's theorem

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In mathematics, and more particularly in polyhedral combinatorics, Eberhard's theorem partially characterizes the multisets of polygons that can form the faces of simple convex polyhedra. It states that, for given numbers of triangles, quadrilaterals, pentagons, heptagons, and other polygons other than hexagons,there exists a convex polyhedron with those given numbers of faces of each type (and an unspecified number of hexagonal faces) if and only if those numbers of polygons obey a linear equation derived from Euler's polyhedral formula.

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  • In mathematics, and more particularly in polyhedral combinatorics, Eberhard's theorem partially characterizes the multisets of polygons that can form the faces of simple convex polyhedra. It states that, for given numbers of triangles, quadrilaterals, pentagons, heptagons, and other polygons other than hexagons,there exists a convex polyhedron with those given numbers of faces of each type (and an unspecified number of hexagonal faces) if and only if those numbers of polygons obey a linear equation derived from Euler's polyhedral formula. The theorem is named after Victor Eberhard, a blind German mathematician, who published it in 1888 in his habilitation thesis and in expanded form in an 1891 book on polyhedra. (en)
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  • In mathematics, and more particularly in polyhedral combinatorics, Eberhard's theorem partially characterizes the multisets of polygons that can form the faces of simple convex polyhedra. It states that, for given numbers of triangles, quadrilaterals, pentagons, heptagons, and other polygons other than hexagons,there exists a convex polyhedron with those given numbers of faces of each type (and an unspecified number of hexagonal faces) if and only if those numbers of polygons obey a linear equation derived from Euler's polyhedral formula. (en)
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  • Eberhard's theorem (en)
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