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Platonic solid

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In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent regular polygons, and the same number of faces meet at each vertex. There are only five such polyhedra:

Kepler's Platonic solid model of the Solar System from Mysterium Cosmographicum (1596)

Icosahedron as a part of Spinoza monument in Amsterdam

A set of polyhedral dice.

Image: Kepler Hexahedron Earth

Geometry

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Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.

A European and an Arab practicing geometry in the 15th century

Woman teaching geometry. Illustration at the beginning of a medieval translation of Euclid's Elements, (c. 1310).

Visual checking of the Pythagorean theorem for the (3, 4, 5) triangle as in the Zhoubi Suanjing 500–200 BC. The Pythagorean theorem is a consequence of the Euclidean metric.

Quintic Calabi–Yau threefold