Question: Is there a tetrahedron or not

Recently found out about Steiner ellipsoids. This is an ellipsoid inscribed in a tetrahedron, and an ellipsoid described near a tetrahedron. One ellipsoid touches the faces of the tetrahedron in centroids, the other ellipsoid touches the planes in vertices of the tetrahedron, and these planes are parallel to the faces.

There is a desire to find out if 4 vertices determine the tetrahedron or not. And it seems Maple answer this question:

restart: with(geom3d):
point(A, 0, 0, 0), point(B, 1, 0, 0), point(C, 0, 0, 1), point(F, 0, 1, 0):
gtetrahedron(T1, [A, B, C, F]):
i := nops(op(0, detail(T1))); 
if i = 1 then print("Ok gtetrahedron") else print("No gtetrahedron") end if:

 I want to stop further execution of the program if the tetrahedron is not determine, for example, when point
B = [0,0,0], but I don’t know how to do it.


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