I was in Edinburgh last week and saw several of these balls in the new
museum (Royal Museum of Scotland and National Museum next door to each
other: one entrance fee admits to both). All the ones I could find on
display had cubic/octahedral or tetrahedral symmetry. There were several
with a larger number of knobs but none had icosahedral/dodecahedral
symmetry. Proof: one knob with 6, not 3 or 5, nearest neighbours (and
insufficient knobs for the "buckyball" pattern).
Do they have some with icosa/dodecahedral symmetry that happened not to be
on display, or are all the balls with more than 8 knobs in a configuration
which is at best a semiregular solid?
John Harper, School of Mathematical and Computing Sciences,
Victoria University, Wellington, New Zealand
e-mail john.harper@vuw.ac.nz phone (+64)(4)471 5341 fax (+64)(4)495 5045
(I'm currently in UK but please continue to use the above e-mail address)