I think it's not possible with your file.

P1, P2, P3, P4 are defined by 3pts for each as all planes 3 points define a plane.
P1 (A, B, H)
P2 (B, C, D)
P3 (D, E, F)
P4 (F, G, H)


The question is : does exist a point P which is on P1, P2, P3 and P4 ?

I think, we have two possibilities to determine it :

1/ Mathematical with a system of equations (each plane is determined by a equation) and its resolution.

2/ MOI (or CAD drawing)
if we do planes P1, P2, P3 and P4 with points A,B,C,D,E,F,G,H with their 3 points, we can do intersections of these 4 planes. If we have only a point... we win and have P !
With your file, the result is a small thetahedron... P does not exist.

My analysis. right or wrong ?