Cute polygon visibility puzzler from Andy Drucker: how many equal-sized equilateral triangles can you place in the plane so that each triangle vertex is visible from each other triangle vertex?

If you're stuck, here's a spoilerific illustration...



Comments:

None:
2007-09-30T18:15:35Z
Thanks, David! It can also be done with infinitely many triangles at once, but the picture is less pretty... -Andy
None:
2007-09-30T18:18:01Z
One additional thing I'd like to know, assuming readers agree with my last statement: must any such infinite arrangement have asymptotic density zero? -A
11011110:
2007-09-30T22:28:43Z
Thanks yourself for a fun puzzle. I assume the answer to your density question must be yes but I don't know how one would go about proving it.