There is none. The number of sides on the bases can always be increased reuslting in an increase in the number of lateral faces. The number of vertices and edges will also increase so there can be no greatest number.
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The greatest number of sides can be any amount of sides.
for any prism , number of ___ + number of vertices = number of edges + ___
The differnence is that a triangular prism has 5 faces and and rectangular prism had 4 faces.
The answer is 3.
There are twelve edges in a rectangular prism.