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In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set.
One might characterise the Greek definition as follows: A regular polygon is a planar figure with all edges equal and all corners equal. A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons, the same number arranged all alike around each vertex.
If a polyhedron has Schläfli symbol {p, q}, then its dual has the symbol {q, p}. Indeed, every combinatorial property of one Platonic solid can be interpreted as another combinatorial property of the dual. One can construct the dual polyhedron by taking the vertices of the dual to be the centers of the faces of the original figure.
If only thirteen polyhedra are to be listed, the definition must use global symmetries of the polyhedron rather than local neighborhoods. In the aftermath, the elongated square gyrobicupola was withdrawn from the Archimedean solids and included into the Johnson solid instead, a convex polyhedron in which all of the faces are regular polygons. [16]
A tetradecahedron is a polyhedron with 14 faces. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon faces. A tetradecahedron is sometimes called a tetrakaidecahedron. [1] [2] No difference in meaning is ascribed. [3] [4] The Greek word kai means 'and'.
Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.) Topologically distinct dodecahedra (excluding pentagonal and rhombic forms) Uniform polyhedra:
In Greek mythology, Polyxo (/ p ə ˈ l ɪ k s oʊ /; Ancient Greek: Πολυξώ, romanized: Poluxṓ), also known as Philozoe (Ancient Greek: Φιλοζώη, romanized: Philozṓē, lit. 'animal-loving' or 'life-loving'), is the wife of the Trojan War hero Tlepolemus, and later the queen of Rhodes, an island in the southeastern Aegean sea.
Greek mythology has changed over time to accommodate the evolution of their culture, of which mythology, both overtly and in its unspoken assumptions, is an index of the changes. In Greek mythology's surviving literary forms, as found mostly at the end of the progressive changes, it is inherently political, as Gilbert Cuthbertson (1975) has argued.