Four is the smallest composite number, its properdivisors being 1 and 2. Four is also a highly composite number. The next highly composite number is 6. Four is the second square number, the second centered triangular number. 4 is the smallest squared prime ( p 2 ) and the only even number in this f orm. It has an aliquot sum of 3 which is itself prime. The aliquot sequence of 4 has 4 members (4, 3, 1, 0) and is accordingly the first member of the 3-aliquot tree. Only one number has an aliquot sum of 4 and that is squared prime 9. The prime factorization of four is two times two. Four is the smallest composite number that is equal to the sum of its prime factors. (As a consequence ofthis, it is the smallest Smith number). However, it is the largest (and only) composite numbern forwhich is false. It is also a Motzkin number. In bases 6 and 12, 4 is a 1-automorphic number. In addition, 2 + 2 = 2 × 2 = 2 2 = 4. Continuing the pattern in Knuth's up-arrow notation , , and so on, for any number of up arrows. A four-sided plane figure is a quadrilateral (quadrangle) orsquare, sometimes also called a tetragon. A circle divided by 4 makes right angles. Because of it, four (4) is the base number ofplane (mathematics) . Fourcardinal directions, four seasons , duodecimal system, and vigesimal system are based on four. A solid figure with four faces is a tetrahedron . The regular tetrahedron is the simplest Platonic solid. A tetrahedron, which can also be called a 3-simplex, has four triangular faces and four vertices. It is the only self-dual regular polyhedron. Four-dimensional s pace is the highest-dimensional space featuring more than three convex regularfigures: Two-dimensional: infinitely many convex regular polygons . T hree-dimensional: five convex regular polyhedra (the five Platonic Solids). F our-dimensional: six convex regular polychora. F ive-dimensional and every higher-dimensional: three regular convex polytopes (regularsimplexes , hypercubes , cross-polytopes ).
