Knowra Platonic solid Platonic solid A convex polyhedron whose faces are congruent regular polygons and whose vertices have identical arrangements of faces. Exactly five Platonic solids exist.
Regular polygon : A polygon with all sides equal and all interior angles equal. Every face of a Platonic solid is a regular polygon.
Interior angle : The angle formed inside a polygon by two adjacent sides. The polygon's interior angle determines how many faces can meet around a vertex.
Tetrahedron : A polyhedron with four triangular faces, four vertices, and six edges. It is the simplest Platonic solid, with three faces meeting at each vertex.
Plato : An ancient Greek philosopher whose dialogues include accounts of mathematical and political ideas. His dialogue Timaeus associated four solids with elements and the fifth with the cosmos.
Buckminsterfullerene : A carbon molecule, C₆₀, whose atoms form a truncated icosahedral cage. Its nearly spherical carbon framework draws on the geometry of an icosahedron.
Polyhedron : A three-dimensional solid bounded by flat polygonal faces. Platonic solids form a precisely defined family of polyhedra.
Dihedral angle : The angle between two intersecting planes, measured between their half-planes within a solid. Each face junction gives a Platonic solid a uniform dihedral angle.
Cube : A regular hexahedron with six square faces, eight vertices, and twelve edges. It is the Platonic solid whose faces are squares.
Timaeus : A dialogue by Plato presenting a cosmological account that uses mathematical structures. It is the source of the traditional elemental associations of the solids.
Icosahedral symmetry : The rotational and reflection symmetries of an icosahedron. It governs the geometry of some molecules, viruses, and engineered structures.
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