Equilateral triangle is the only triangle with integer sides and three rational angles as measured in degrees. The equilateral triangle is the only acute triangle that is similar to its orthic triangle (with vertices at the feet of the altitudes) (the heptagonal triangle being the only obtuse one). Equilateral triangles are found in many other geometric constructs. The intersection of circles whose centers are a radius width apart is a pair of equilateral arches, each of which can be inscribed with an equilateral triangle. They form faces of regular and uniform polyhedra. Three of the five Platonic solids are composed of equilateral
Euler angles Guthrie Tait and George H. Bryan. It is the convention normally used for aerospace applications, so that zero degrees elevation represents the horizontal attitude. Tait–Bryan angles represent the orientation of the aircraft with respect to the world frame. When dealing with other vehicles, different axes conventions are possible. The definitions and notations used for Tait-Bryan angles are similar to those described above for proper Euler angles (geometrical definition, intrinsic rotation definition, extrinsic rotation definition). The only difference is that Tait–Bryan angles represent rotations about three distinct axes (e.g. "x-y-z", or "x-y’-z″"), while proper Euler angles use the same axis for