A curriculum introducing the concentric hierarchy of volumes 1, 3, 4, 6, 20 with other volumes (including irrational) interspersed, in the context of closest packing (non-XYZ lattice), does not have to purge itself of XYZ. It goes directly to the imagination and fills your head. Cartesian coordinates are welcome (but we glance at Quadrays for a different perspective).

You get comfortable with these geometric concepts early (in connection with natural and human designed architectures) and that means you get the history too: this bold futurist (tons of materials) returned from obscurity…