Use Perpendicular Projection to Prove Some Properties of Disphenoid and Some of Its Applications in Engineering

An isosceles of the tetrahedron, also called disphenoid, is a tetrahedron where all four faces are congruent acute-angled triangles and every two edges that are opposite each other have the same length (Desphenoid—Wikipedia, the Free Encyclopedia, p. 1, https://en.wikipedia.org/wiki/Disphenoid , 1). If the four faces of the disphenoid are equilateral triangles, it is a regular tetrahedron. So, the regular tetrahedron is a special case of the disphenoid. A disphenoid has some characterizations and properties. They are widely used in the design of steel structures. This paper aims to solve some spatial geometry problems of a disphenoid to apply to the process of calculating, designing, and making technical drawings of it quickly and accurately.