Triangle Group

This simple demo allows the user to experiment with a wide variety of 2-dimensional triangle groups. In the process the users gains a direct experience the three different standard planar metric geometries — euclidean, elliptic, and hyperbolic. The left and right arrow keys cycle through the archetypal groups 236, 235 and 237, while a wider choice of groups is available under the “Groups” menu. The ‘2’ key toggles between display of elliptic case as a projective plane (flat) or as a sphere (double covering of elliptic plane). The displayed tessellation gotten by reflecting a point P across the three sides of the triangle can be changed by dragging this point while holding down the right mouse. The left mouse translates in the ambient metric. Because Triangle Group is completely written in Java you’ll be able to easily deploy it across a variety of platforms.