5-4-3
The above polyhedron was first
described in Professor Bonnie Stewart's "Adventures Among the
Toroids" (2nd Edition page 157), where it receives the name m*
, although Professor Stewart was not
specifically searching for Acrohedra. It was rediscovered by Professor John Conway
as part of his specific
search for a solution for the 5-4-3 acron. In having only 12
faces it edged out the previous contender, the Stewart
G3, by just one face. See here for more on the Stewart G3.
The minimal non-self-intersecting case can be
improved upon if we permit self-intersection. Dr Richard Klitzing has studied the
facets of the small ditrigonal icosidodecahedron
amongst
which was the above 9-faced figure.
Dr Klitzing informs me that he has to date only studied facets with a three-fold
or five-fold
symmetry, so this result may still be improved upon.
The full results of Dr Klitzing's work
on faceting a number of the uniform polyhedra are
hosted by Ulrich Mikloweit here.
Back: to acrohedra