If all sides have equal lengths and all the angles have equal measures the is a what?

Then this shape is called a REGULAR POLYGON. It's exact name will depend on the number of sides it has- if three, then it'll be an EQUILATERAL TRIANGLE, if four a SQUARE, if five a PENTAGON, if six a HEXAGON, and so on. But if all sides & angles are equal, then it's a REGULAR (whatever).