Question: How to generate a better looking sphere with a chessboard pattern

In the attachment is an attempt with undesireable rendering artefacts

I did not use color functions because I intend to export the black fields of the ball to stl format to use them for a better visualisation of spinning spheres in MapleSim.

A related question: The generating function for the chessboard looks complicated to me. Maybe there is a more elegant way to do it.

Chessboard_sphere.mw

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