 
Summary: The Penrose dodecahedron revisited
Jordan E. Massad and P. K. Aravind
Physics Department, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
Received 9 June 1998; accepted 14 October 1998
This paper gives an elementary account of the ``Penrose dodecahedron,'' a set of 40 states of a
spin3
2 particle used by Zimba and Penrose Stud. Hist. Phil. Sci. 24, 697720 1993 to give a
proof of Bell's nonlocality theorem. The Penrose rays are constructed here from the rotation
operator of a spin3
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 ``prooftree'' argument
is used to establish the noncolorability of the Penrose rays and hence prove Bell's theorem. © 1999
American Association of Physics Teachers.
I. INTRODUCTION
Some years ago Zimba and Penrose1
ZP gave an inge
nious proof of Bell's nonlocality theorem using a special set
of states of a spin3
2 particle. Because these states have a
