48 (number)

48 is a highly composite number, and a Størmer number.^[1]

By a classical result of Honsberger, the number of incongruent integer-sided triangles of perimeter ${\displaystyle m}$ is given by the equations ${\displaystyle {\tfrac {m^{2}}{48}}}$ for even ${\displaystyle m}$, and ${\displaystyle {\tfrac {(m+3)^{2}}{48}}}$ for odd ${\displaystyle m}$.^[2]

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.

Forty-eight may also refer to:

• In Chinese numerology, 48 is an auspicious number meaning 'determined to prosper', or simply 'prosperity', which is good for business.^[3]
• '48 is a slang term in Palestinian Arabic for parts of Israel or Palestine not under the control of the State of Palestine. Arab people from those parts are colloquially known as 48-Arabs (Arabic: عرب ٤٨, romanized: ‘Arab Thamāniya wa-Arba‘īn).