A four-sided plane figure is a quadrilateral, sometimes also called a tetragon. A solid figure with four faces is a tetrahedron. The regular tetrahedron is the simplest Platonic solid.
The smallest non-cyclicgroup has four elements; it is the Klein four-group. Four is also the order of the smallest non-trivial groups that are not simple.
A flat two-dimensional map can always be colored using only four different colors so that all adjacent regions are colored with a different color; three colors are not sufficient. This is the four color theorem.
Lagrange's four-square theorem[?] states that every positive integer can be written as the sum of at most four square numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares.