Abstract. Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S² and the torus T, and the not orientable projective space P² and Klein's bottle K. Two families of 3nj graphs admit embeddings of minimal genus into S² and P². Their dual 2-skeletons are shown to be triangulations of these surfaces.

PACS numbers: 04.20.Gz, 02.40.−k, 02.40.Sf

Print publication: Issue 40 (11 October 2002)
Received 20 May 2002, in final form 27 May 2002
Published 24 September 2002