You are given eight points in three-dimensional space, please check if they can form a cube.
A cube is a regular hexahedron, bounded by six square faces, with three meeting at each vertex.
The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 100$$$), denoting the number of test cases.
For each test case, each of the following eight lines containing three integers $$$x,y,z$$$ ($$$-100 \leq x,y,z \leq 100$$$), denoting the coordinates of the eight points, respectively.
For each test case, output a single line "YES" if the points can form a cube, or "NO" if they don't.
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 -6 -2 5 9 10 12 -11 11 -9 4 8 -2 -16 9 7 -1 21 -7 -6 19 10 -1 0 0 0 0 2 2 1 0 0 1 0 2 0 2 0 0 0 2 1 2 0 1 2 2 0
NO YES NO
Name |
---|