The periodic table also displays a peculiar property: the invariant groups in d dimensions are identical to those in d − − 1 dimensions but in a different symmetry class. Among the complex symmetry classes, the invariant group for A in d dimensions is the same as that for AIII in d − − 1 dimensions, and vice versa. One can also imagine arranging each of the eight real symmetry classes on the Cartesian plane such that the x coordinate is T 2 if time reversal symmetry is present and 0 if it is absent, and the y coordinate is C 2 if particle hole symmetry is present and 0 if it is absent. Then the invariant group in d dimensions for a certain real symmetry class is the same as the invariant group in d − − 1 dimensions for the symmetry class directly one space clockwise. This phenomenon was termed the "Bott clock" by Alexei Kitaev, in reference to the Bott periodicity theorem.