There are three 6 digit numbers with the following properties applicable to each:

1. All digits are unique.
2. The first three digits ABC form a triangular number as do the latter three, DEF; both are multiples of 3.
3. The digital root/sum of the first triangular number is greater than that of the second.
4. Three consecutive digits form the difference of the triangular numbers, either being ascending or descending.

Identify the three 6 digit numbers.