About integer-valued variants of the theta and 6<i>j</i> symbols

This article contains essentially a rewriting of several properties two well-known quantities, the so-called theta symbol (or triangular symbol), which is rational, and 6 j symbol, usually irrational, in terms related integer-valued functions called gon tet. Existence these avatars, sharing most essential with their more popular partners, although known fact, often overlooked. The tet are easier to obtain, or formulate, than those corresponding symbols both classical quantum situations. Their evaluation also simpler (this paper displays number explicit formulas procedures that may speed up some computer programs). These unusual do not appear be discussed literature, but features reflect real-valued many places. Some we shall discuss seem, however, new, particular relations between function inverse Hilbert matrices.