The “twirl”, stella octangula and mixed state entanglement

Abstract A simple group theoretical explanation is given of the “twirl” operation introduced by Bennett et al. [Phys. Rev. Lett. 76 (1996) 722]. Following this, some aspects of mixed state entanglement discussed by Horodecki et al. [Phys. Rev. A 54 (1996) 1838], Peres [Phys. Rev. Lett. 77 (1996) 1413] and Bennett et al. [Phys. Rev. A 54 (1996) 3852] are unified within the framework of a geometrical diagram introduced by Horodecki et al.