# Bell-ringing methods as polyhedra

• Published in 2015
In his popular book "The Bob Caller's companion" Mr. Steve Coleman notes how any bell-ringing method can be represented as a directed graph, with a node for each lead head and an edge for each plain lead or bob lead. He further notes that if the graph can be drawn without any of the edges crossing, then it can be made into a polyhedron, with the edges and nodes of the graph being the edges and nodes of the polyhedron. He gives Grandsire Doubles and Plain Bob Doubles as examples of this. This left me asking myself the question: how many different polyhedra are there whose nodes and edges map onto the graph of the lead-heads of a ringing method, popular or otherwise? I enumerated the possible cases for lead heads of plain doubles and minor methods and found the following cases, some of which have polyhedral graphs and some of which do not.

### BibTeX entry

@online{Bellringingmethodsaspolyhedra,
title = {Bell-ringing methods as polyhedra},
abstract = { In his popular book "The Bob Caller's companion" Mr. Steve Coleman notes how any bell-ringing method can be represented as a directed graph, with a node for each lead head and an edge for each plain lead or bob lead. He further notes that if the graph can be drawn without any of the edges crossing, then it can be made into a polyhedron, with the edges and nodes of the graph being the edges and nodes of the polyhedron. He gives Grandsire Doubles and Plain Bob Doubles as examples of this.

This left me asking myself the question: how many different polyhedra are there whose nodes and edges map onto the graph of the lead-heads of a ringing method, popular or otherwise? I enumerated the possible cases for lead heads of plain doubles and minor methods and found the following cases, some of which have polyhedral graphs and some of which do not.},
url = {https://www.geos.ed.ac.uk/{\~{}}hcp/bells/},
year = 2015,
author = {Hugh C. Pumphrey},
comment = {},
urldate = {2021-11-20},
collections = {combinatorics,easily-explained,fun-maths-facts,the-groups-group,things-to-make-and-do}
}