We have an old problem Equilateral Triangle which asked can an equilateral triangle have all three of its vertices on lattice points on a 2-D plane or in 3-D space. Those answers were "no" and "yes", respectively.

I ask can a regular pentagon be placed in 2-D with all five of its vertices on lattice points? If that is not possible what about 3-D space?

The quickest way to dispense of the 2d case is to use the argument given by Jerry in the old problem:

Posted by Jer on 2024-04-05 11:56:19