You can depict a triangular number, T(N), by writing one 1 on a line, then two 2's on the line below, then three 3's on the line below that, and so on until N N's. You end up with a triangle of T(N) numbers, hence the name.
For example, T(1) through T(5):
1
1
22
1
22
333
1
22
333
4444
1
22
333
4444
55555
To keep things nicely formatted we'll use the last digit of the number for N > 9, so T(11) would be:
1
22
333
4444
55555
666666
7777777
88888888
999999999
0000000000
11111111111
Now pretend like each row of digits in one of these triangles is a 1-by-something polyomino tile that can be moved and rotated. Call that a row-tile.
For all triangles beyond T(2) it is possible to rearrange its row-tiles into a W×H rectangle where W > 1 and H > 1. This is because there are no prime Triangular numbers above N > 2. So, for N > 2, we can make a rectangle from a triangle!
(We're ignoring rectangles with a dimension of 1 on one side since those would be trivial by putting every row on one line.)
Here is a possible rectangle arrangement for each of T(3) through T(11). Notice how the pattern could be continued indefinitely since every odd N (except 3) reuses the layout of N - 1.
N = 3
333
221
N = 4
44441
33322
N = 5
55555
44441
33322
N = 6
6666661
5555522
4444333
N = 7
7777777
6666661
5555522
4444333
N = 8
888888881
777777722
666666333
555554444
N = 9
999999999
888888881
777777722
666666333
555554444
N = 10
00000000001
99999999922
88888888333
77777774444
66666655555
N = 11
11111111111
00000000001
99999999922
88888888333
77777774444
66666655555
However, there are plenty of other ways one could arrange the row-tiles into a rectangle, perhaps with different dimensions or by rotating some row-tiles vertically. For example, these are also perfectly valid:
N = 3
13
23
23
N = 4
33312
44442
N = 5
543
543
543
541
522
N = 7
77777776666661
55555444433322
N = 8
888888881223
666666555553
444477777773
N = 11
50000000000
52266666634
57777777134
58888888834
59999999994
11111111111
Challenge
Your task in this challenge is to take in a positive integer N > 2 and output a rectangle made from the row-tiles of the triangles of T(N), as demonstrated above.
As shown above, remember that:
The area of the rectangle will be T(N).
The width and height of the rectangle must both be greater than 1.
Row-tiles can be rotated horizontally or vertically.
Every row-tile must be depicted using the last digit of the number it represents.
Every row-tile must be fully intact and within the bounds of the rectangle.
The output can be a string, 2D array, or matrix, but the numbers must be just digits from 0 through 9.
The output does not need to be deterministic. It's ok if multiple runs produce multiple, valid rectangles.
The shortest code in bytes wins!