Generalised vector products and metrical trigonometry of a tetrahedron

Abstract

We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear form over a general field, not of characteristic two. This gives us algebraic analogs of many classical formulas, as well as new insights and results. In particular we derive original relations for a tri-rectangular tetrahedron.