Calculating all possible planes from an array of (x,y,z) points

Can you be specific about what you need help with? In a "divide and conquer" type approach, here's a generic breakdown of how I see performing this task.

A) Generate all pemutations of 3 integers from 1-9. An internet search should provide several different descriptions of algorithms for generating these permutations (probably mostly in symbolic languages like VBA rather than spreadsheet formulas). I'm sure spreadsheet formulas could be adapted to these algorithms, if that is necessary.
B) Extract the three X, the three Y, and the three Z values from the larger set based on a given permutation generated in A. I would tend to use the INDEX() function for this: https://support.office.com/en-us/art...2-b56b061328bd
C) Use the LINEST() function to generate the coefficients of the plane (z=Ax+By+C). https://support.office.com/en-us/art...a-fa7abf772b6d

Which of these steps are you stuck on?

Generate all pemutations

Combinations