The Making of Logoglyphs, Part I

I was doodling one day on a crossword puzzle, filling in the squares like this: I got to thinking about how many different ways I could combine these four triangular shapes in a 2 by 2 grid.I came up with 256.

Some more doodling got me from this:to this:
to this:
which I thought would make a cool sculpture--maybe out of curved pieces of copper tubing--if I put a couple of the shapes together.

But how do I find the best combinations of 256 different symbols? To narrow it down I picked the 26 I liked best and assigned each to a letter of the alphabet. That made it easier to find the best pairings.

A little more doodling got me from this:to this:to this:
A bunch of those shapes, arranged in a 2 by 2, 3 by 3, or 3 by 4 grid, looked really cool, sort of in perspective, but not:
Part II coming soon.