rho: (0, 0, 0, 0, 2, 0, 0, 0)
center: (8, 12, 16, 24, 20, 15, 10, 5)
lattice point: True

rho: (0, 0, 0, 2, 0, 0, 0, 2)
center: (4, 6, 8, 12, 19/2, 7, 9/2, 2)
lattice point: False

rho: (0, 0, 0, 2, 0, 0, 2, 0)
center: (3, 9/2, 6, 9, 7, 5, 3, 3/2)
lattice point: False

rho: (0, 0, 0, 2, 0, 0, 2, 2)
center: (3, 9/2, 6, 9, 13/2, 4, 3/2, 1/2)
lattice point: False

rho: (2, 0, 0, 2, 0, 0, 2, 0)
center: (1, 3, 7/2, 6, 5, 4, 3, 3/2)
lattice point: False

rho: (2, 0, 0, 2, 0, 0, 2, 2)
center: (1, 3, 7/2, 6, 9/2, 3, 3/2, 1/2)
lattice point: False

rho: (2, 0, 0, 2, 0, 2, 0, 2)
center: (1, 2, 5/2, 4, 3, 2, 3/2, 1)
lattice point: False

rho: (2, 0, 0, 2, 0, 2, 2, 2)
center: (1, 2, 5/2, 4, 5/2, 1, 1/2, 1/2)
lattice point: False

rho: (2, 2, 2, 0, 2, 0, 2, 2)
center: (1/2, 1, 1, 2, 2, 3/2, 1, 1/2)
lattice point: False

rho: (2, 2, 2, 0, 2, 2, 2, 2)
center: (1/2, 1, 1, 3/2, 1, 1/2, 1/2, 1/2)
lattice point: False

rho: (2, 2, 2, 2, 2, 2, 2, 2)
center: (1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)
lattice point: False