You can "change sides" by adding number of sides (say, from a triangle to a square) or by adding side length (say, from area 4 to 9).

Hint 2

The 1 in each line represents the first letter of that line's word, because one dot can represent the smallest n-gon for any n.
Each page also corresponds to one word.

Hint 3

35 is the fifth pentagonal number, while 36 is the third tridecagonal number, and 246 is the sixth octadecagonal number. (Did we mention NUMBERs?)
A general formula might help you explain the negative numbers (and save a bunch of time).