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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.
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:
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 In the aftermath, the elongated square gyrobicupola was withdrawn from the Archimedean solids and included into the Johnson solid instead, a convex polyhedron in which all of the faces are regular polygons.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]
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.
A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron was named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Δ. [1] Deltahedra can be categorized by the property of convexity. The simplest convex deltahedron is the regular tetrahedron, a pyramid with four equilateral ...
In ancient Greek religion and mythology, the twelve Olympians are the major deities of the Greek pantheon, commonly considered to be Zeus, Poseidon, Hera, Demeter, Aphrodite, Athena, Artemis, Apollo, Ares, Hephaestus, Hermes, and either Hestia or Dionysus. [2] They were called Olympians because, according to tradition, they resided on Mount ...