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   Rect. Parallelepiped, Cube Formulas   

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also see Defining Geometric Figures

A parallelepiped (alternate spelling parallelopiped) is a polyhedron with six faces bounded by three pairs of parallel planes, so all its faces are parallelograms. It is also a prism the base of which is a parallelogram.

 Rectangular Parallelepiped

    A three-dimensional figure all of whose face angles are right angles,
    so all its faces are rectangles and all its dihedral angles are right angles.
    (A dihedral angle is an angle created by two intersecting planes.)
 
Edges: a, b, c
Diagonal: d
Total surface area (total area of all
     the faces of the figure): T
Volume: V
 

    d = sqrt(a2+b2+c2)
T = 2(ab+ac+bc)
V = abc
Face diagonals sqrt(a2+b2),
     sqrt(a2+c2), sqrt(b2+c2)
 

 Cube

  A three-dimensional figure with
six congruent square sides.

a = b = c
 
    d = a sqrt(3)
T = 6a2
V = a3

Face diagonal a sqrt(2)  

 

To read about parallelepipeds and cubes, visit:

Ask Dr. Math: What is a parallelepiped?
Encarta Online: Prism
Eric Weisstein's World of Mathematics: Cube

And see: Regular Polyhedra

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