I was messing around with slopes, trying to make a jigsaw-puzzle.

I discovered a problem: the 45 degree slopes don’t exactly match. If I try to align a slope and an inverted slope, the bricks aren’t all aligned. The top image shows the bricks aligned: there is a growing gap between the slopes rising from left to right. The bottom image shows the slopes aligned, exaggerating the effect in the bricks. 

When applying this to my jigsaw puzzle, the effect looks untidy:

There is a simple solution – turn one of the pieces upside down. Then the slopes and the bricks line up very nicely.

The result is reasonably satisfactory. Unfortunately the gap where the studs are (at the top here) is less than a plate tall, so I can’t easily fill it with a normal piece. The gap at the bottom is even thinner. But everything is nice and square.

EDIT – immediately after posting this article, a friend suggested I read about a new 1×2 slope piece that LEGO produce. There are two of these: the older new one has exactly the same slope angle (and problem) as the traditional 1×2 slope, but the newer new one has a different angle, and solves the alignment problem without having to turn one part of the jigsaw upside down.