Library/Geometry/Solid geometry/Polyhedra and spatial polygons/Polyhedra and polygons (other)

Polyhedra and polygons (other)

Overview
Important

Polyhedra are three-dimensional solids with flat polygonal faces, straight edges, and vertices. Beyond the regular and common types (like cubes and pyramids), there are many other polyhedra, including irregular polyhedra, star polyhedra, and polyhedra with faces of different types of polygons.

Important properties

  • A polyhedron's faces are polygons.

  • The sum of the face angles at each vertex is less than 360°.

  • Euler's formula relates the number of vertices (V), edges (E), and faces (F): V - E + F = 2 for convex polyhedra.

  • Some polyhedra have faces that are not all the same shape or size.