represents a parallelepiped with origin p and directions vi.
- Parallelepiped is also known as parallelogram, rhombohedron, and parallelotope.
- Parallelepiped represents , where the vectors vi have to be linearly independent.
- Parallelepiped can be used as a geometric region and graphics primitive.
- Parallelepiped can be used in Graphics and Graphics3D.
- In graphics, the point p and vectors vi can be Scaled and Dynamic expressions.
- Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.
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Basic Examples (3)
A Parallelepiped in 3D:
Solve equations over a Parallelepiped:
For a full-dimensional Parallelepiped, the measure is easily computed from the vectors:
For a lower-dimensional Parallelepiped, the square root of the Gram determinant is used:
The Gram determinant is the determinant of dotted with its Transpose:
Any full-dimensional Parallelepiped can tile space: