I have the sphere x^2 + y^2 + z^2 =( 33*sqrt(3))^2 and I want to select four points on a sphere to make a regular tetrahedron so that its coordinates are integer numbers. I see this question is here https://mathematica.stackexchange.com/questions/289123/how-can-i-select-four-points-on-a-sphere-to-make-a-regular-tetrahedron-so-that-i
Time to get result is a problem. 

This is old question https://www.mapleprimes.com/questions/208909-Code-For-Integer-Points-On-Sphere. Now I see this question at here 
https://mathematica.stackexchange.com/questions/288956/how-can-i-get-all-squares-on-this-sphere-so-that-its-coordinates-are-integer-num
 My idea is select all diameters which diameters are perpendicularly from the sphere (x-2)^2 + (y-4)^2 + (z-6)^2 = 15^2. How can I tell Maple to do that?

I am trying to find a polygon that its graph take this four points as extra point. 
I tried
f := x -> a*x^7 + b*x^6 + c*x^5 + d*x^4 + k*x^3 + l*x^2 + m*x + n;
solve([f(-2) = -5, f(5) = -6, f(6) = 1, f(-1) = 2, eval(diff(f(x), x), x = -2) = 0, eval(diff(f(x), x), x = 5) = 0, eval(diff(f(x), x), x = 6) = 0, eval(diff(f(x), x), x = -1) = 0], [a, b, c, d, k, l, m, n]);

I get. Is there a polymial with lower degree take this four point as extra points?

When I input
restart;
a := 2;
b := 3;
p := x^2 - a*x - b*x +a*b ;
I get p := x^2 - 5*x + 6
How can I get x^2 - 2 x - 3x + 6.
General question. I have (a,b) in a list [[2,3],[-3,7],[9,10]]. How to subtitute them to get the result
[[x^2 - 2x - 3x + 6, x^2 + 3x - 7x -21, x^2 - 9x - 10x + 90]? 

I am trying to draw this pictures in LaTeX, then I need to find their parametric equations. How can I get them?