Singular Manual: tetrahedronGroup

| ##### 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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