Synergetics coordinates

Synergetics coordinates have each unit as a simplex: a triangle, tetrahedron, pentachoron, etc., in fact a regular simplex, rather than like Cartesian coordinates which use a rectangle or box. Therefore synergetics coordinates are ordered n-tuples in $R\_+^ncup\; \{0\}$ which is equivalent to $R^n-1$.

For example, regular triangular coordinates are of the form $(x,y,z)$ such that $x,y,z$ are equal to or greater than 0.

Similarly, regular tetrahedral coordinates are of the form $(w,x,y,z)$ such that $w,x,y,z$ are equal to or greater than 0.