In my research for new #Mathart , I have developed a nice chart to show the different types of triangles that exist (1). The idea was to classify them by how they look visually. The chart starts from a horizontal segment which will be the largest side of the triangle (or one of the larger). Then each point of the chart represents the triangle formed by joining that point to the ends of the segment (in fact if we are not interested in distinguish chirality half of the chart would suffice, but I find aesthetically nicer the symmetric version). By looking at it I have realized that isosceles triangles can be split into two visually different types: pointed and squashed. In pointed isosceles triangles the different side is smaller than the other, in squashed ones the opposite. Of course obtuse and right isosceles triangles are always squashed. The second image is what you obtain if the initial side is not necessarily the largest (colour codes are the same).
(1) Which is not new, I have found something similar in Hebrew: https://commons.m.wikimedia.org/wiki/File:Moduli_space_of_triangles_1_he.svg
By the way, it would be nice if someone could develop an image search which understand 2D geometry.
