[r-t] Methods as polyhedra
mark at snowtiger.net
Wed Apr 9 20:13:53 UTC 2008
Ah! Just thought. Of course if we are looking at nodes rather than leads,
then things are different.
Two leads are the same - a call on one will elicit the same transformation
as the same call on the other. But two nodes are not the same. Instead,
nodes fall in to categories: the nodes from say W->H have a different set of
transformations to the nodes from M->W.
Effectively, a restriction such as "tenors together" adds an asymmetry to
the search space network, and means we must map to a polyhedron with a
similar asymmetry. In particular, a vertex-transitive polyhedron is no good,
because all the vertices are certainly not the same. We would need to find a
polyhedron with n different classes of vertices, where n equals the number
of node types.
So that is something very different, and I suppose Mr King might be right
that we can find them... still assuming edges do not cross. How we actually
go about that is another matter.
More information about the ringing-theory