Reminds me of the book Gnomon: From Pharaohs to Fractals and Number: From Ahmes to Cantor, by Midhat Gazalé.
I likewise favor figurate numbers (e.g. triangular, square…) followed by polyhedral numbers (e.g. tetrahedral, pyramidal…), starting early, as we’re building that left-right brain bridge (lexical-graphical, algebraic-geometric) without needing any fancy coordinate systems (yet).
An anchoring number sequence we always get to is: 1, 12, 42, 92…, which applies to the cuboctahedron and icosahedron both. Showing exactly why this sequence applies to both is easiest with an animation (cue IMU logo movie).
So now we’re into both crystallography (CCP) and virology (capsomere counts). No parent will tell us this isn’t core STEM.