Definition

1. Noun:
   • A Platonic solid: A regular convex polyhedron is a three-dimensional shape where all faces are identical, regular polygons, and the same number of faces meet at each vertex. There are exactly five such solids.

Usage

• The term is used in geometry to classify and describe the five specific, perfectly symmetrical three-dimensional shapes.
• It is a formal, academic term. In less formal contexts, the more common term "Platonic solid" is often used.

Examples

• Noun:
  • A cube is a regular convex polyhedron with six square faces.
  • The tetrahedron, cube, octahedron, dodecahedron, and icosahedron are the only five regular convex polyhedra.
  • In his geometry class, he learned the properties of each regular convex polyhedron.

Advanced Usage

• Mathematical Proof: The term is central to the theorem proving that only five such solids can exist.
  • Euclid's Elements provides a mathematical proof for the existence of exactly five regular convex polyhedra.

Variants and Related Words

• Platonic solid (n): A synonym for , named after the ancient Greek philosopher Plato.
  • Plato associated each of the four classical elements with a Platonic solid.
• Regular polyhedron (n): A more general term that can sometimes be used interchangeably, though it strictly emphasizes the regularity of faces and vertices.
• Convex polyhedron (n): A broader category of 3D shapes where any line segment connecting two points inside the shape lies entirely within it; all belong to this category.

Synonyms

• Platonic solid: The most common synonym.
• Regular polyhedron: A closely related term.
• Cosmic figure (historical/archaic): An older term sometimes used.

Related Concepts (Not Phrasal Verbs or Idioms)

• Dual polyhedron: A concept where the vertices of one correspond to the faces of another (e.g., the cube and octahedron are duals).
• Schläfli symbol: A notation used to represent (e.g., {4,3} for a cube).

Noun

1. any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent