regular convex polyhedron

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regular convex polyhedron

A student holds a model of a regular convex polyhedron in geometry class.

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).
regular convex polyhedron

A student holds a model of a regular convex polyhedron in geometry class.

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

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