# ip(v,w) = dot product of vectors
# xRy(v,w) = is x related to y by the conditions I need?
# XRY(V,W) = are all v in V and w in W pairwise related by xRy? (where V and W are lists of vectors)


N1 = list(#of all of the vectors i am interested in#); n1 = len(N1);
for vv1 in range(0,n1):
    for vv2 in range(0,n1):
        if ip(N1[vv1],N1[vv2])==0:
            for vv3 in range(0,n1):
                if ip(N1[vv1],N1[vv3])==0 and ip(N1[vv2],N1[vv3])==0:
                    basez1 = list([N1[vv1],N1[vv2],N1[vv3]]);
                    print basez1; print vv1,vv2,vv3; print 'basez1...................\n';
                    for ww1 in range(0,n1):
                        if xRy(N1[ww1],N1[vv1]) and xRy(N1[ww1],N1[vv2]) and xRy(N1[ww1],N1[vv3]):
                            for ww2 in range(0,n1):
                                if ip(N1[ww1],N1[ww2])==0:
                                    if xRy(N1[ww2],N1[vv1]) and xRy(N1[ww2],N1[vv2]) and xRy(N1[ww2],N1[vv3]):
                                        for ww3 in range(0,n1):
                                            if ip(N1[ww1],N1[ww3])==0 and ip(N1[ww2],N1[ww3])==0:
                                                if xRy(N1[ww3],N1[vv1]) and xRy(N1[ww3],N1[vv2]) and xRy(N1[ww3],N1[vv3]):
                                                    testbasez2 = list([N1[ww1],N1[ww2],N1[ww3]]);
                                                    if XRY(basez1,testbasez2):
                                                        basez2 = testbasez2;
                                                        print basez2; print ww1,ww2,ww3; print 'basez2-------------------\n';
                                                        for xx1 in range(0,n1):
                                                            if xRy(N1[xx1],N1[vv1]) and xRy(N1[xx1],N1[vv2]) and xRy(N1[xx1],N1[vv3]) and xRy(N1[xx1],N1[ww1]) and xRy(N1[xx1],N1[ww2]) and xRy(N1[xx1],N1[ww3]):
                                                                    for xx2 in range(0,n1):
                                                                        if ip(N1[xx1],N1[xx2])==0:
                                                                            if xRy(N1[xx2],N1[vv1]) and xRy(N1[xx2],N1[vv2]) and xRy(N1[xx2],N1[vv3]) and xRy(N1[xx2],N1[ww1]) and xRy(N1[xx2],N1[ww2]) and xRy(N1[xx2],N1[ww3]):
                                                                                for xx3 in range(0,n1):
                                                                                    if ip(N1[xx1],N1[xx3])==0 and ip(N1[xx2],N1[xx3])==0:
                                                                                        if xRy(N1[xx3],N1[vv1]) and xRy(N1[xx3],N1[vv2]) and xRy(N1[xx3],N1[vv3]) and xRy(N1[xx3],N1[ww1]) and xRy(N1[xx3],N1[ww2]) and xRy(N1[xx3],N1[ww3]):
                                                                                            testbasez3 = list([N1[xx1],N1[xx2],N1[xx3]]);
                                                                                            if XRY(basez1,testbasez3) and XRY(basez2,testbasez3):
                                                                                                basez3 = testbasez3;
                                                                                                print basez3; print xx1,xx2,xx3; print 'basez3=====================\n';