These notes contain essentially a rewriting of several properties of two well-known quantities, the so-called theta symbol (or triangular symbol), which is rational, and the $6j$ symbol, which is usually irrational, in terms of two related integer-valued functions called gon and tet. Existence of these related integer-valued avatars, sharing most essential properties with their more popular partners, although a known fact, is often overlooked. The properties of gon and tet are easier to obtain, or to formulate, than those of the corresponding theta and $6j$ symbols, both in the classical and quantum situations. Their evaluation is also simpler (the paper displays a number of explicit formulae and evaluation procedures that may speed up some computer programs). These two integer-valued functions are unusual, in that their properties do not appear to be often discussed in the literature, but their features reflect those of related real-valued functions discussed in many places. Although our presentation is non-standard, the purpose of these notes is mostly pedagogical. Some of the properties that we shall discuss seem however to be new, in particular a relation with inverse Hilbert matrices. For its most part, the text does not require any familiarity with any specific scientific domain besides elementary arithmetics.