Concept
20 (twenty; Roman numeral XX) is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score. Twenty is a pronic number, as it is the product of consecutive integers, namely 4 and 5. It is the third composite number to be the product of a squared prime and a prime, and also the second member of the (22)q family in this form. 20 is the smallest primitive abundant number. 20 is the third tetrahedral number. 20 is the basis for vigesimal number systems. 20 is the number of parallelogram polyominoes with 5 cells. 20 is the number of moves (quarter or half turns) required to optimally solve a Rubik's Cube in the worst case. 20 is the length of a side of the fifth smallest right triangle that forms a primitive Pythagorean triple, (20,21,29). This is the second Pythagorean triple that can be formed using Pell numbers where and are one unit apart. There are twenty edge-to-edge 2-uniform tilings by convex regular polygons, which are uniform tessellations of the plane containing 2 orbits of vertices. The largest number of faces a Platonic solid can have is twenty faces, which make up a regular icosahedron. A dodecahedron, on the other hand, has twenty vertices, likewise the most a regular polyhedron can have. There are a total of 20 regular and semiregular polyhedra, aside from the infinite family of semiregular prisms and antiprisms that exists in the third dimension: the 5 Platonic solids, and 15 Archimedean solids (including chiral forms of the snub cube and snub dodecahedron). There are also four uniform compound polyhedra that contain twenty polyhedra (UC13, UC14, UC19, UC33), which is the most any such solids can have; while another twenty uniform compounds contain five polyhedra. The compound of twenty octahedra can be obtained by orienting two pairs of compounds of ten octahedra, which can also coincide to yield a regular compound of five octahedra. In total, there are 20 semiregular polytopes that only exist up through the 8th dimension, which include 13 Archimedean solids and 7 Gosset polytopes (without counting enantiomorphs, or semiregular prisms and antiprisms).