We have the following figure:
The following points are given:
$$N= (8.98,99.82,54.25); M= (31.16,97.78,54.25); \\ L= (74.65,70.61,54.25); K= (84.85,51.91,54.25); \\ J= (9.07,95.48,119.35); I= (30.77,93.44,119.35); \\ H= (70.96,68.36,119.35); G= (81.81,50,119.35) $$
and also the following planes are given:
$$E(ABN): -9446,05x + 911,57y+ 48,17z = 8781,16; \\ E(NMS): 110,67x +1203,27y-193,13z=110626,19; \\ E(HQP):3026,52x - 4952,5y + 0,21z=-123765,61; \\ E(DCI):X= (25.77 / 40.74 / 182.28) +r (3.05 / 31/ 0) +s(5 /52,7 / -62.93) \\ E(KLP):X=(84.85 / 51.91 / 54.25) +t (-10.2 / 18.7 / 0) +p (-17.58 / 14.19 / -54.25) \\ E(FOA):X= (63.36 / 38.71 / 182.28) +v(14.76 / 9.03 / -128.28) + w (-63.36 / -38.71 / 0) \\ E(GHL):X= (81.81 / 50 / 119.35) +d (-10.85 / 18.36 / 0) +c (-7.16 / 20.61 / -65.1) \\ E(IJN):X= (30.77 / 93.82 / 119.35) +m (-21.7 / 2.04 / 0) +t(-21.79 / 6.38 / -65.1) $$
How can we determine the coordinates of the other points?
You can put a cutting plane through the figure parallel to $ABC$ near the top or parallel to $QRS$ near the bottom, truncate the figure at the cutting plane, and relabel the points so that you have a new figure that looks "just like" the old one (except for small changes to the locations of some points) and satisfies all the given equations.
So I think the answer is that you cannot determine the coordinates of the other points.