In elementary geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. The word polyhedron comes from the Classical Greek πολύεδρον, as poly- (stem of πολύς, many) + -hedron (form of ἕδρα, base or seat).olyhedra with congruent regular faces of six or more sides are all non-convex, because the vertex of three regular hexagons defines a plane. The total number of convex polyhedra with equal regular faces is thus ten, comprising the five Platonic solids and the five non-uniform deltahedra.