Singular Manual: tetrahedronGroup

| #### 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 Tsaranov-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*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

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