[r-t] Methods as polyhedra

[King, Peter R]

Sorry I've been busy so it has taken to get back. Of course, I never
said the polyhedron has to exist in 3 dimensions. In fact I don't think
it can, I think the minimum for what I had in mind is 4D, which I think
alters the argument. However, I still haven't made my mind up as to
whether or not this representation is useful! 

> -----Original Message-----
> From: ringing-theory-bounces at bellringers.net 
> [mailto:ringing-theory-bounces at bellringers.net] On Behalf Of 
> Mark Davies
> Sent: 09 April 2008 21:14
> To: ringing-theory at bellringers.net
> Subject: [r-t] Methods as polyhedra
> 
> 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.
> 
> MBD 
> 
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