An equilateral triangle is a regular triangle, just as a square is a regular rectangle, and you can have regular pentagons and so on: the sides are all the same length. 'Perfect' is used for various things in mathematics: 625 is a perfect square, because its square root is a whole number, whereas 624 is not; and we can define perfect cubes similarly. A perfect number is one whose smaller factors add up to it: 6 = 1 + 2 + 3, and 28 = 1 + 2 + 4 + 7 + 14. These are the common uses of 'perfect' I can think of.