What did Kepler do for the field of mathematics?

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What were some of Kepler's mathematical concepts? After a little research, I have discovered Kepler's conjecture (the sphere packing), how ellipses (foci, eccentricity, etc) correspond to Kepler's first law, and a few formulas here and there. What else did he do?
 
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The first ideas explaining crystals, hexagaonal close packing, snowflakes. In book called 'New year's gift of a snowflake'. Had right idea though missed something and didn't get it quite right.

Some fancy polyhedra.
 

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