I think what the word “quadrays” has over “tetrays” is its close association with the word “quadrant”.
Those groomed to be hypercross dogmatists (starting with “space is 3D”) aren’t used to imagining dividing space into four symmetrically identical sectors, by means of four “fences” defined by any pair of quadrays.
Go back in your mind to K-12 and ask yourself at what point did any textbook…
