What is a parallelepiped?
Q: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms.
Q: What other term is sometimes used to refer to a parallelepiped?
A: The term "rhomboid" is also sometimes used with the same meaning as "parallelepiped."
Q: How does a parallelepiped relate to a parallelogram?
A: A parallelepiped relates to a parallelogram in the same way that a cube relates to a square or a cuboid relates to a rectangle.
Q: Does the definition of a parallelepiped in Euclidean geometry include all four related concepts?
A: Yes, in Euclidean geometry the definition of a parallelepiped encompasses all four related concepts: parallelepiped, parallelogram, cube, and square.
Q: What is the context of affine geometry?
A: The context of affine geometry is one in which angles are not differentiated.
Q: In the context of affine geometry, what shapes are included in the definition of a parallelepiped?
A: In affine geometry, the definition of a parallelepiped only admits parallelograms and parallelepipeds.
Q: What are three equivalent definitions of a parallelepiped?
A: Three equivalent definitions of a parallelepiped are: a polyhedron with six faces, each of which is a parallelogram; a hexahedron with three pairs of parallel faces; and a prism of which the base is a parallelogram.
