See notes for some instructions and pictures for flat joining method.
For each cube, the lightest color goes on the lower left (diamond rotated downhill), and the darkest on the lower right (diamond rotated uphill). The mid-shade color goes on the top of each cube. This will make it look like each cube is facing to the left.
When making the top diamond (middle color), leave a long enough tail at the beginning AND end to sew to the strip above and below it. For the other diamonds, leave enough yarn to sew one side together (for the strips). Can sew the lightest and darkest diamonds together into a strip, and then sew in the top ones in between the strips to connect everything.
Joining method - see pictures. Similar to a mattress stitch. Pretty invisible, and totally flat! Bring needle from back to front into alternating stitches, leaving them loose for a few stitches (so you can see where to go next -- one stitch per row-end), and pull tight every few stitches. Works great! As I progressed, I started sticking my needle closer to the edge to minimize the amount of “bump” in the seam. Tedious. So. Very. Tedious.
After the whole deal was stitched together, it took some crochet-edging trickery to get things as even as possible, and it’s still not great (the white yarn had a larger gauge than the others, it’s all wonky on the edges), but darn it all, THIS THING IS DONE. I LOVE IT WITH ALL OF MY BEING, AND I AM NEVER EVER EVER GOING THROUGH THIS PATTERN AGAIN! :)