0048

48 is a highly composite number, and a Størmer number. By a classical result of Honsberger, the number of incongruent integer-sided triangles of perimeter m {\displaystyle m} is given by the equations m 2 48 {\displaystyle {\tfrac {m^{2}}{48}}} for even m {\displaystyle m}, and ( m + 3 ) 2 48 {\displaystyle {\tfrac {(m+3)^{2}}{48}}} for odd m {\displaystyle m}. 48 is the order of full octahedral symmetry, which describes three-dimensional mirror symmetries associated with the regular octahedron and cube. There are 48 symmetries of a cube.