Josef Kurschak constructed a beautiful tile that constructs a dodecagon that makes several interesting observations possible. (See this sketch for that construction: [url]http://www.geogebratube.org/material/show/id/49694[/url])[br][br]In that sketch he inscribes four equilateral triangles in a tile. Well one of the things mathematicians love to ask is "What If?" What if it wasn't an equilateral triangle?[br][br]This sketch lets you see isosceles or right triangles (in the constrained option) or totally free exploration.