Search results
Results from the WOW.Com Content Network
A parallelepiped has three sets of four parallel edges; the edges within each set are of equal length. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations). Since each face has point symmetry, a parallelepiped is a zonohedron.
The volume of a rhombohedron ... is a simplification of the volume of a parallelepiped, and is given by ... Four points forming non-adjacent vertices of a ...
[note 1] That is, for a point in the lattice r, the arrangement of points appears the same from r′ = r + T → as from r. [4] Since the primitive cell is defined by the primitive axes (vectors) a → 1, a → 2, a → 3, the volume V p of the primitive cell is given by the parallelepiped from the above axes as
The three vectors spanning a parallelepiped have triple product equal to its volume. (However, beware that the direction of the arrows in this diagram are incorrect.) In exterior algebra and geometric algebra the exterior product of two vectors is a bivector, while the exterior product of three vectors is a trivector. A bivector is an oriented ...
Expressed symmetrically as 4 points on the ... to 1 / 6 of the volume of any parallelepiped that shares ... any given tetrahedron is a point now known ...
Each point in a point lattice has periodicity i.e., each point is identical and has the same surroundings. There exist an infinite number of point lattices for a given vector lattice as any arbitrary origin X 0 {\displaystyle X_{0}} can be chosen and paired with the lattice vectors of the vector lattice.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
This is because the n-dimensional dV element is in general a parallelepiped in the new coordinate system, and the n-volume of a parallelepiped is the determinant of its edge vectors. The Jacobian can also be used to determine the stability of equilibria for systems of differential equations by approximating behavior near an equilibrium point.