Triangle their internal angles, measured here in degrees. A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral. Triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise (see Non-planar triangles, below). In rigorous treatments, a triangle is therefore called a "2-simplex" (see also Polytope). Elementary facts about triangles were presented by Euclid in books 1–4
Wythoff symbol and formula_7, represent the corners of the Schwarz triangle used in the construction, which are formula_8, formula_9 and formula_10 radians respectively. The triangle is also represented with the same numbers, written formula_11. The vertical bar in the symbol specifies a categorical position of the generator point within the fundamental triangle according to the following: In this notation the mirrors are labeled by the reflection-order of the opposite vertex. The formula_18 values are listed "before" the bar if the corresponding mirror is active. The one "impossible" symbol formula_19 implies the generator point is on all mirrors, which is only possible if