Can an equilateral triangle have vertices at integral lattice points?

*Integral lattice points are such points as (101, 254) or (3453, 12), but not points such as (123.4, 1) or (√2, 5)*
If you can't find a solution in the 2D Cartesian plane, can you find one in a 3 (or more) dimensional space?

(In reply to

re: short answers by Penny)

No , Mam

For a) the irrationality speaks for itself.

For b) I have just imagined a triangle (0;0),(2*a,0), (a, sqrt3*a) rotated 60 degrees around 0X, creating (0;0;0)(2a;0;0)(a;a;2*a), 'a' being an integer.

a votre service

a