A long time ago a similar question arose in the sci.math newsgroup. I worked it out that in order to make a loop out of dodecahedra, one has to use sets of three dodecahedra in a row, as shown (four times) in the picture above -- otherwise one introduces a set of rotations in R^3 which has no relations which we can use to get the first and last faces to line up. See http://www.math-atlas.org/98/dodec_prf

dave

A long time ago a similar question arose in the sci.math newsgroup. I worked it out that in order to make a loop out of dodecahedra, one has to use sets of three dodecahedra in a row, as shown (four times) in the picture above -- otherwise one introduces a set of rotations in R^3 which has no relations which we can use to get the first and last faces to line up. See this link.

dave