File:16 choose 2 triangle colored.svg

Array of the ${\displaystyle {\tbinom {16}{2}}=T_{15}=120}$ two-element subsets of a 16-element set (Binomial coefficient, Triangular number)

Each hexagon represents a set ${\displaystyle \{a,b\}}$ for which ${\displaystyle a,b\in \{0...15\}}$ with a pair ${\displaystyle (a,b)}$ for which ${\displaystyle a<b}$. The figures are nibble shorthands.

Below the two figures the same pair is indicated by highlighting two among 16 positions.

The colors indicate the Hamming distance of the two numbers (by how many bits their binary representations differ).

For Hamming distances 1 and 3 the weights of the two numbers (1s in their binary representations) have different parity.
For 2 and 4 they have the same. So brown and gray come in two shades to express if it is even or odd.
Light represents even. Light brown (3, 15) has weights (2, 4) and parities (even, even).