Search results
Results from the WOW.Com Content Network
The vertex arrangement of the 16-cell honeycomb is called the D 4 lattice or F 4 lattice. [2] The vertices of this lattice are the centers of the 3-spheres in the densest known packing of equal spheres in 4-space; [3] its kissing number is 24, which is also the same as the kissing number in R 4, as proved by Oleg Musin in 2003.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
In this case local rigidity never holds. For cocompact lattices a small deformation remains a cocompact lattice but it may not be conjugated to the original one (see Teichmüller space for more detail). Non-cocompact lattices are virtually free and hence have non-lattice deformations.
[4] More generally, any complete chain is a completely distributive lattice. [5] The power set lattice ((),) for any set X is a completely distributive lattice. [1] For every poset C, there is a free completely distributive lattice over C. [3] See the section on Free completely distributive lattices above.
In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima.Most of these apply to partially ordered sets that are at least lattices, but the concept can in fact reasonably be generalized to semilattices as well.
Besides distributive lattices, examples of modular lattices are the lattice of submodules of a module (hence modular), the lattice of two-sided ideals of a ring, and the lattice of normal subgroups of a group. The set of first-order terms with the ordering "is more specific than" is a non-modular lattice used in automated reasoning.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... The 2 x 2, 3 x 3, and 4 x 4 subnet kagome lattices. The 2 × 2 subnet is also ...
Dynamical Theory of Crystal Lattices is a book in solid state physics, authored collaboratively by Max Born and Kun Huang.The book was originally started by Born in c. 1940, and was finished in the 1950s by Huang in consultation with Born.