Could a coordinate system, with tetrahedral symmetry be more convenient than Cartesian coordinates?
The [sp.sup.3] hybrid is a well-known geometrical entity whose equal distribution of electron densities allows the construction of more complex bonds toward other [sp.sup.3] carbons, possibly in different hybridization states, or towards other atoms, some of which also displaying the [sp.sup.3] tetrahedral symmetry. Tetrahedral carbon could be presented with a centre of mass in the gravicentre of a tetrahedron, with four specific directions oriented in such a way as to form an angle of 109[degrees] 28' between any two of the four axes.
The present study is a reflection of what the world could look like if we did use the coordinates based on the four axes forming the tetrahedral symmetry.