Standardised co-ordinate geometry applied to affine rational trigonometry of a tetrahedron

Abstract: The idea of standardised co-ordinates in three-dimensional affine space is defined, by way of the Standard tetrahedron. By performing an affine map on a general tetrahedron, we may replace the study of a general tetrahedron over a specific metrical structure with the study of a specific tetrahedron over a general metrical structure. Using the framework of Wildberger's rational trigonometry as well as the definitions of generalised scalar and vector products in the author's previous work, we will compute the various trigonometric invariants associated to the Standard tetrahedron, with the purpose of proving some more complicated results which are difficult to prove without this mechanism.