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The triakis truncated tetrahedron is a convex space-filling polyhedron which is the shape of the Voronoi cell of carbon atoms in diamond. It can be constructed from the ...

A schematic mathematical illustration showing the relationships between or properties of mathematical objects.

Also called Chvátal's art gallery theorem. If the walls of an art gallery are made up of n straight line segments, then the entire gallery can always be supervised by |_n/3_| ...

Cluster analysis is a technique used for classification of data in which data elements are partitioned into groups called clusters that represent collections of data elements ...

The Engel polyhedra are two 38-faced plesiohedra (and hence space-filling) discovered by Engel (Engel 1981; Engel 1986, p. 220; Grünbaum and Shephard 1980; Senechal 1990, ...

Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...

Sphere tetrahedron picking is the selection of quadruples of of points corresponding to vertices of a tetrahedron with vertices on the surface of a sphere. n random ...

A space-filling polyhedron is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that ...

The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points p_1, ..., p_N, the convex hull C is then given by the ...

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. ...