Given the triangle ABC where angle ABC=90 then angles BAC+BCA=90 degrees. There's 89*2=178 possible combinations that solve it correctly if you stay within 2D. <grin> Escher implies an interest in 3D triangles or hyperbolic geometry. Good luck.
Correcting a mistake. There's only 89 combinations that solve your triangle question. I realized it right after the edit window expired but thought I'd wait and see if anyone else caught it. Then I tired of waiting. So what's up with the triangle? Where are you going with this?