The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created … See more

A convex polyhedron is a Platonic solid if and only if all three of the following requirements are met.
• All of its faces are congruent convex regular polygons.
• None of its faces intersect except at th… See more

The classical result is that only five convex regular polyhedra exist. Two common arguments below demonstrate no more than five Platonic solids can exist, but positively demonstrating the existence of any given s… See more

There are a number of angles associated with each Platonic solid. The dihedral angle is the interior angle between any two face planes. The dihedral angle, θ, of the solid {p,q} is given by the formula
This is som… See more

Every polyhedron has a dual (or "polar") polyhedron with faces and vertices interchanged. The dual of every Platonic solid is another Platonic solid, so that we can arrange the five solids into dual pairs.
• The … See more