Question: How to choose four points on the sphere so that the triangle is not a right triangle?

I want to choose four points A, B, C, D on the sphere  (x-2)^2 + (y-4)^2 +(z-6)^2 -81=0 from the list L so that there are not any the right triangle are formed from the points A, B, C, D. How to get it? I tried


> restart:


eqS:=Equation(sphere(S,(x-2)^2 + (y-4)^2 +(z-6)^2 -81=0,[x,y,z],'centername'=T)):


for x from -5 to 10  do

for y from -5 to 10  do

for z from -5 to 10  do  if  x<>xcoord(T) and y<>ycoord(T) and z <> zcoord(T) and   type(x,integer) and type(y,integer)and type(z,integer) and eqS then

L:=[op(L), [x,y,z]] fi;

od: od: od:




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