Can equipotential lines cross?

Equipotential lines can never cross. Equipotential lines indicate a certain voltage and are always constant, so for two equipotential lines to cross would mean that the area they cover has two separate voltages at the same time, which is not possible.

To better understand why equipotential lines cannot cross, imagine the contour lines on a map going over a mountain. Contour lines on a map indicate a constant elevation, rather than a constant voltage like equipotential lines. It would be impossible for them to cross, because a point on a mountain cannot have two separate heights at the same time.