From the pixels[] array which is singular in dimensions we can extrapolate a two dimensional locale in the following fashion:
Code:

int x = pixels.length % width;
int y = pixels.length / width;
 

If a length of string can become a square, surely it can become a cube:
Code:

x = (n % (width * height) % width;
y = (n % (width * height)) / width;
z = n / (width * height);
 

I felt from this point I should be able to create an algorithm that given "n" a point on a one dimensional array, one should be able to give an array of dimensions (d[]) and receive an array of the where that point is in your defined abstract space.
Code:

 //4d
 x = (n % (d[0] * d[1] * d[2])) % (d[0] * d[1]) % d[0];
 y = (n % (d[0] * d[1] * d[2])) % (d[0] * d[1]) / d[0];
 z = (n % (d[0] * d[1] * d[2])) / (d[0] * d[1]);
 h = n / (d[0] * d[1] * d[2]);
 
 //5d
 0 = (n % (d[0] * d[1] * d[2] * d[3])) % (d[0] * d[1] * d[2]) % (d[0] * d[1]) % d[0];
 1 = (n % (d[0] * d[1] * d[2] * d[3])) % (d[0] * d[1] * d[2]) % (d[0] * d[1]) / d[0];
 2 = (n % (d[0] * d[1] * d[2] * d[3])) % (d[0] * d[1] * d[2]) / (d[0] * d[1]);
 3 = (n % (d[0] * d[1] * d[2] * d[3])) / (d[0] * d[1] * d[2]);
 4 = n / (d[0] * d[1] * d[2] * d[3]);
 

There's a logical pattern to what's going on here, I can't see how to implement it just now. I have tested each of these equations and they seem to hold true. The trick seems to be to modulo through the dimensions till you're at point where you can measure down (except when measuring x) and then divide by the multiple of the dimensions below that dimension. Any suggestions?