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1998

Penrose dodecahedron

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The Penrose Dodecahedron Revisited, Padmanabhan Aravind, Jordan Massad Oct 1998

The Penrose Dodecahedron Revisited, Padmanabhan Aravind, Jordan Massad

Padmanabhan K. Aravind

This paper gives an elementary account of the ‘‘Penrose dodecahedron,’’ a set of 40 states of a spin- 3 2 particle used by Zimba and Penrose @Stud. Hist. Phil. Sci. 24, 697–720 ~1993!# to give a proof of Bell’s nonlocality theorem. The Penrose rays are constructed here from the rotation operator of a spin- 3 2 particle and the geometry of a dodecahedron, and their orthogonality properties are derived and illustrated from a couple of different viewpoints. After recalling how the proof of Bell’s theorem can be reduced to a coloring problem on the Penrose rays, a ...