7.10.2.27 tetrahedronGroup

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
- varying g produces a family of examples

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

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