Definition

1. Noun:
   • A solid geometric figure in three dimensions that is completely bounded by flat polygonal surfaces called faces. The faces meet at straight-line segments called edges, and the edges meet at points called vertices.

Examples of Usage

• Noun:
  • A cube is a common example of a polyhedron.
  • The architect designed a building with the complex shape of an irregular polyhedron.
  • In geometry class, we learned to calculate the volume of a polyhedron.

Advanced Usage

• Regular Polyhedron: A polyhedron whose faces are all identical regular polygons and whose vertices are all identical. There are only five convex regular polyhedra (Platonic solids).
  • The tetrahedron, cube, and dodecahedron are all regular polyhedra.
• Convex Polyhedron: A polyhedron where any line segment connecting two points on its surface lies entirely inside or on the polyhedron.
  • Most basic geometric shapes, like prisms and pyramids, are convex polyhedra.
• Euler's Formula for Polyhedra: A fundamental theorem stating that for a convex polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the formula V - E + F = 2.
  • We used Euler's formula to verify the structure of the model polyhedron.

Variants and Related Words

• Polyhedral (adjective): Of or relating to a polyhedron; having the shape or form of a polyhedron.
  • The sculpture had a striking polyhedral form.
• Polyhedra (noun): The standard plural form of , often used in academic or technical contexts.
  • The study focused on the properties of various polyhedra.

Synonyms

• Solid (in a geometric context): A three-dimensional figure.
• Geometric solid: A three-dimensional geometric shape.

Different Meanings

• The term is highly specific to geometry and three-dimensional space. It does not have common metaphorical or idiomatic meanings outside of mathematical and related technical fields (e.g., computer graphics, crystallography).

Noun

1. a solid figure bounded by plane polygons or faces