find an integer I which can be classified as Prime, Triangle, Square or Cube, comprised of unique digits and when the digits are rearranged, one of those categories applies.
Then specifically apply that rule to fill the table with the lowest values possible per category (integer I) with its anagram being larger, in the lower cell per category.
Note: It may not be possible to offer solutions for all asymetric categories.
You might care also to offer some suggestions whereby some integers, without rearranging, may fall into another category - 36 (S), 36 (T); 729 (S), 729 (C).
Note that colours by row and column are category-defined.
