View example sentences and word forms for Parallelotope.
Parallelotope
Parallelotope meaning
A generalization of parallelogram and parallelepiped into a figure of arbitrary dimensionality.
Example sentences (7)
Similarly, the volume of any n- simplex that shares n converging edges of a parallelotope has a volume equal to one 1/ n! of the volume of that parallelotope.
Specifically in n-dimensional space it is called n-dimensional parallelotope, or simply n-parallelotope.
Hypervolume of an n-parallelotope spanned by n vectors For vectors and spanning a parallelogram we have : with the result that is linear in the product of the "altitude" and the "base" of the parallelogram, that is, its area.
Inversion in this point leaves the n-parallelotope unchanged.
It could be any shape, although the volume equals that of the parallelotope.
The diagonals of an n-parallelotope intersect at one point and are bisected by this point.
The same arguments are also valid for a general parallelotope, except the isometry between the simplexes.