Points A(1, 1, 1), B(-2, 4, 1), C(1, -5, 5) and D(2, 2, 5) are the vertices of a square if all sides are of equal measure.
Apply distance formula, and find the distance between all the points:
From above results, AB = BC = CD = AD, and AC = BD
Hence vertices A, B, C, D form a square.