13 Facts About Platonic solids

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.

Platonic solids are prominent in the philosophy of Plato, their namesake.

Andreas Speiser has advocated the view that the construction of the 5 regular Platonic solids is the chief goal of the deductive system canonized in the Elements.

In Mysterium Cosmographicum, published in 1596, Kepler proposed a model of the Solar System in which the five Platonic solids were set inside one another and separated by a series of inscribed and circumscribed spheres.

Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids enclosed within a sphere that represented the orbit of Saturn.

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Platonic solids discovered the Kepler solids, which are two nonconvex regular polyhedra.

Platonic solids centered at the origin, simple Cartesian coordinates of the vertices are given below.

Two common arguments below demonstrate no more than five Platonic solids can exist, but positively demonstrating the existence of any given solid is a separate question—one that requires an explicit construction.

The dual of every Platonic solid is another Platonic solid, so that we can arrange the five solids into dual pairs.

Symmetry groups of the Platonic solids are a special class of three-dimensional point groups known as polyhedral groups.

Several Platonic solids hydrocarbons have been synthesised, including cubane and dodecahedrane and not tetrahedrane.

Platonic solids are often used to make dice, because dice of these shapes can be made fair.

Johnson Platonic solids are convex polyhedra which have regular faces but are not uniform.