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An algebra <L; ^ , v > is called a lattice if L is a nonempty set, ^ and v are binary operations on L, both ^ and v are idempotent, commutative, and associative, and they ...

A dipyramid having a hexagonal base. The volume of a hexagonal pyramid having a regular hexagon with side length a as a base and of half-height h is therefore V=sqrt(3)a^2h. ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

A polygonal number and 6-polygonal number of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... (OEIS A000384). The generating function for the hexagonal numbers is ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

A number which is simultaneously a heptagonal number Hep_n and hexagonal number Hex_m. Such numbers exist when 1/2n(5n-3)=m(2m-1). (1) Completing the square and rearranging ...

A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height h is a special case of the formula for a regular n-gonal pyramid with n=6, given by ...

A hexagonal prism is a prism composed of two hexagonal bases and six rectangular sides. It is an octahedron. The regular right hexagonal prism is a space-filling polyhedron. ...

A hexagonal antiprism is an antiprism having hexagons as its bases. A stretched hexagonal antiprism is the convex hull of the tetrahedron 3-compound. The dual polyhedron of ...

A hexagonal grid is a grid formed by a tessellation of regular hexagons. Boards made of hexagonal grids are often found in strategy and role-playing games because of the lack ...