84
Eighty-four is the sum of the first seven triangular numbers (making it a tetrahedral number), as well as the sum of a twin prime (41 + 43). Being thrice a perfect number, 84 is itself a semiperfect number.
Eighty-four is also the lim sup of the largest finite subgroup of the mapping class group of a genus g surface divided by g.
A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces
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