[r-t] Methods as polyhedra

Mark Davies 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.


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