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7.7.8.0. tetrahedronGroup
Procedure from library fpalgebras.lib (see fpalgebras_lib).

Usage:
tetrahedronGroup(g,d); g an integer, d an integer

Return:
ring

Note:
- the ring contains the ideal I, which contains the required relations - g gives the number of the example (1 - 5)
- d gives the degreebound for the Letterplace ring

This is a family

The examples are found in
Classification of the finite generalized tetrahedron groups by Gerhard Rosenberger and Martin Scheer.
The 5 examples are denoted in Proposition 1.9 and concern finite generalized tetrahedron group in the Tsarnarov-case, which are not equivalent to a presentation for an ordinary tetrahedron group.

Example:
 
LIB "fpalgebras.lib";
def R = tetrahedronGroup(3,5); setring R;
I;
==> I[1]=x(1)*x(2)*x(3)+1
==> I[2]=y(1)*y(2)*y(3)+1
==> I[3]=z(1)*z(2)*z(3)+1
==> I[4]=x(1)*y(2)*x(3)*y(4)+1
==> I[5]=x(1)*z(2)*x(3)*z(4)+1
==> I[6]=y(1)*z(2)*y(3)*z(4)+1


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