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In this posting we introduce the concept of antisymmetry of Cube positions: antisymmetric positions include self-inverse positions as a special case. We show that the size of Cube Space is reduced by approximately a factor of 2 after taking account of positions that are related to one another by antisymmetry. The "new" real size of Cube Space is found to be 450541810590509978.

[Contribution also posted on sci.math]