Hexagonal Days occur when your day age is a centred hexagonal number.

A centred hexagonal number, or hex number, is a centred figurate number that represents a hexagon with a dot in the centre and all other dots surrounding the centre dot in a hexagonal lattice.

Strictly, a hexagonal number is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.

We choose to use centred hexagonal numbers to calculate our Hexagonal Days because all (outlined) hexagonal numbers are also triangular numbers and these are already commemorated in our Triangular Days.