
7.10.2.27 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
 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 Tsaranovcase, 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*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

