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A polyhedron (plural polyhedra or polyhedrons) is a geometric solid in three dimensions with flat faces and straight edges. The word polyhedron comes from the Classical Greek πολύεδρον, as poly (stem of πολύς, "many") + edron (form of έδρα, "base", "seat", or "face").
Defining a polyhedron as a solid bounded by flat faces and straight edges is not very precise and, to a modern mathematician, quite unsatisfactory. Grünbaum (1994, p. 43) observed, "The Original Sin in the theory of polyhedra goes back to Euclid, and through Kepler, Poinsot, Cauchy and many others ... [in that] at each stage ... the writers failed to define what are the 'polyhedra' ...." Since then rigorous definitions of "polyhedron" have been given within particular contexts. However such definitions are seldom compatible in other contexts.
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