The greatest distance between any two vertices of a rectangular prism with dimensions 8 cm by 9 cm by 12 cm is the diagonal distance of the rectangular prism. This distance can be found using the Pythagorean theorem. The diagonal distance is √(8^2 + 9^2 + 12^2) = √(64 + 81 + 144) = √289 = 17 cm.
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