 These include the Calabi triangle (a triangle with three congruent inscribed squares), the golden triangle and golden gnomon (two isosceles triangles whose sides and base are in the golden ratio), the 80-80-20 triangle appearing in the Langley’s Adventitious Angles puzzle, and the 30-30-120 triangle of the triakis triangular tiling.Five Catalan solids, the triakis tetrahedron, triakis octahedron, tetrakis hexahedron, pentakis dodecahedron, and triakis icosahedron, each have isosceles-triangle faces, as do infinitely many pyramids and bipyramids.For any isosceles triangle, the following six line segments coincide