What are the names for geometric arrangements like 'quincunx'?

Solution 1:

I believe that tetractys should match this request.

Tetractys is a triangular figure consisting of ten points arranged in four rows, which is the geometrical representation of the fourth triangular number.

Solution 2:

“Similar related names that were derived the same way” is unfortunately ambiguous, but if you mean are there other geometric arrangements with names formed by prefixing a Latin geometric term with a Latin numeric prefix, the answer is yes. For example, from etymonline, triangle derived “from O.Fr. triangle (13c.), from L. triangulum “triangle,” from neut. of adj. triangulus “three-cornered,” from tri- “three” (see tri-) + angulus “corner, angle”, and quadrangle “from O.Fr. quadrangle (13c.), from L.L. quadrangulum “four-sided figure,” properly neuter of Latin adjective quadrangulus “having four quarters,” from L. quattuor “four” (see four) + angulus “angle”. Pentagon and nonagon also are from Latin. However, pentangle and hexagon are from the Greek.