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Dual polyhedron
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In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. Such dual figures remain combinatorial or abstract polyhedra, but not all can also be constructed as geometric polyhedra. Starting with any given polyhedron, the dual of its dual is the original polyhedron.
The dual of a Platonic solid can be constructed by connecting the face centers. In general this creates only a topological dual. Images from Kepler's
The dual of a Platonic solid can be constructed by connecting the face centers. In general this creates only a topological dual. Images from Kepler's Harmonices Mundi (1619)
Polyhedron
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In geometry, a polyhedron is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
Convex polyhedron blocks on display at the Universum museum in Mexico City
Convex polyhedron blocks on display at the Universum museum in Mexico City
Problem 14 of the Moscow Mathematical Papyrus, on calculating the volume of a frustum
Problem 14 of the Moscow Mathematical Papyrus, on calculating the volume of a frustum
14-sided die from the Warring States period
14-sided die from the Warring States period
Doppio ritratto, attributed to Jacopo de' Barbari, depicting Luca Pacioli and a student studying a glass rhombicuboctahedron half-filled with water.
Doppio ritratto, attributed to Jacopo de' Barbari, depicting Luca Pacioli and a student studying a glass rhombicuboctahedron half-filled with water.