Dual polyhedron
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In geometry, every polyhedron is associated with a second dual structure, wherein the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to
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 Harmonice Mundi (1619)
Polyhedron
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In geometry, a polyhedron is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boun
Dual polyhedron
…In geometry, every polyhedron is associated with a second dual structure, wherein the vertices of one correspond to the faces of the other and the edges between pairs of vertices…
An ideal regular octahedron in the Poincaré ball model of hyperbolic space (sphere at infinity not shown). All dihedral angles of this shape are right angles.
Problem 14 of the Moscow Mathematical Papyrus, on calculating the volume of a frustum
Fourteen 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.