Library/Geometry/Solid geometry/Parallelepipeds

Parallelepipeds

Overview
Important

A parallelepiped is a three-dimensional solid with six faces, where each face is a parallelogram. Opposite faces are parallel and congruent. Parallelepipeds are a type of prism, specifically those whose bases are parallelograms.

Important properties

  • All faces are parallelograms.

  • Opposite faces are parallel and congruent.

  • The volume of a parallelepiped with adjacent edges of lengths aa, bb, cc and angles between them can be calculated using the scalar triple product.

  • A rectangular box (cuboid) is a special case where all angles are right angles.

Deeper topics