Trigonal Superspace Groups

copyright (c) Jul. 1999 by Akiji Yamamoto

3166 R3(00p,00q)0

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3167 R3(00p,00q).0t. equivalent group: R3(00p,00q).0t. R3(00p,00q).t0. R3(00p,00q).tt. R3(00p,00q).tt. R3(00p,00q).t0. R3(00p,00q).tt. R3(00p,00q).tt.

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,1/3+u; -x+y,-x,z,t,2/3+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n 00lmn:n=3n 00lmn:2n=3n

3168 R3(qp0,-pr0)0

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3169 P3(00p,00q)0

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u;

3170 P3(00p,00q).0t. equivalent group: P3(00p,00q).0t. P3(00p,00q).t0. P3(00p,00q).tt. P3(00p,00q).tt. P3(00p,00q).t0. P3(00p,00q).tt. P3(00p,00q).tt.

x,y,z,t,u; -y,x-y,z,t,1/3+u; -x+y,-x,z,t,2/3+u;

00lmn:n=3n 00lmn:2n=3n

3171 P31(00p,00q)0 equivalent group: P31(00p,00q).0t. P31(00p,00q).0t. P31(00p,00q).t0. P31(00p,00q).tt. P31(00p,00q).tt. P31(00p,00q).t0. P31(00p,00q).tt. P31(00p,00q).tt. P3(00p,00q)0 P3(00p,00q).0t. P3(00p,00q).0t. P3(00p,00q).t0. P3(00p,00q).tt. P3(00p,00q).tt. P3(00p,00q).t0. P3(00p,00q).tt. P3(00p,00q).tt.

x,y,z,t,u; -y,x-y,1/3+z,t,u; -x+y,-x,2/3+z,t,u;

00lmn:l=3n 00lmn:2l=3n

3172 P3(00p,1/31/3q)0

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n

3173 P3(00p,1/31/3q).t0. equivalent group: P3(00p,1/31/3q).t0.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,1/3+t,u; -x+y,-x,z,2/3+t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 00lmn:m=3n 00lmn:2m=3n

3174 P31(00p,1/31/3q)0 equivalent group: P31(00p,1/31/3q).t0. P31(00p,1/31/3q).t0. P3(00p,1/31/3q)0 P3(00p,1/31/3q).t0. P3(00p,1/31/3q).t0.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,1/3+z,t,u; -x+y,-x,2/3+z,t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 00lmn:l=3n 00lmn:2l=3n

3175 P3(r-q0,qp0)0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t;

3176 P31(r-q0,qp0)0 equivalent group: P3(r-q0,qp0)0

x,y,z,t,u; -y,x-y,1/3+z,-u,t-u; -x+y,-x,2/3+z,-t+u,-t;

00l00:l=3n 00l00:2l=3n

3177 P3(r-q1/3,qp2/3)0

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3178 R-3(00p,00q)0

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3179 R-3(qp0,-pr0)0

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3180 P-3(00p,00q)0

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u;

3181 P-3(00p,1/31/3q)0

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n

3182 P-3(r-q0,qp0)0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t;

3183 P-3(r-q1/3,qp2/3)0

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3184 R32(00p,00q)00

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; y,x,-z,-t,-u; x-y,-y,-z,-t,-u; -x,-x+y,-z,-t,-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3185 R32(00p,00q).0t.0 equivalent group: R32(00p,00q).0t.0 R32(00p,00q).t0.0 R32(00p,00q).tt.0 R32(00p,00q).tt.0 R32(00p,00q).t0.0 R32(00p,00q).tt.0 R32(00p,00q).tt.0

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,1/3+u; -x+y,-x,z,t,2/3+u; y,x,-z,-t,-u; x-y,-y,-z,-t,2/3-u; -x,-x+y,-z,-t,1/3-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n 00lmn:n=3n 00lmn:2n=3n

3186 R32(-p2p0,-2pp0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,-u,-t; x-y,-y,-z,-t+u,u; -x,-x+y,-z,t,t-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3187 R32(p00,0p0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,u,t; x-y,-y,-z,t-u,-u; -x,-x+y,-z,-t,-t+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3188 P312(00p,00q)000

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,-z,-t,-u; -x+y,y,-z,-t,-u; x,x-y,-z,-t,-u;

3189 P312(00p,00q).0t.00 equivalent group: P312(00p,00q).0t.00 P312(00p,00q).t0.00 P312(00p,00q).tt.00 P312(00p,00q).tt.00 P312(00p,00q).t0.00 P312(00p,00q).tt.00 P312(00p,00q).tt.00

x,y,z,t,u; -y,x-y,z,t,1/3+u; -x+y,-x,z,t,2/3+u; -y,-x,-z,-t,-u; -x+y,y,-z,-t,2/3-u; x,x-y,-z,-t,1/3-u;

00lmn:n=3n 00lmn:2n=3n

3190 P3112(00p,00q)000 equivalent group: P3112(00p,00q).0t.00 P3112(00p,00q).0t.00 P3112(00p,00q).t0.00 P3112(00p,00q).tt.00 P3112(00p,00q).tt.00 P3112(00p,00q).t0.00 P3112(00p,00q).tt.00 P3112(00p,00q).tt.00 P312(00p,00q)000 P312(00p,00q).0t.00 P312(00p,00q).0t.00 P312(00p,00q).t0.00 P312(00p,00q).tt.00 P312(00p,00q).tt.00 P312(00p,00q).t0.00 P312(00p,00q).tt.00 P312(00p,00q).tt.00

x,y,z,t,u; -y,x-y,1/3+z,t,u; -x+y,-x,2/3+z,t,u; -y,-x,-z,-t,-u; -x+y,y,2/3-z,-t,-u; x,x-y,1/3-z,-t,-u;

00lmn:l=3n 00lmn:2l=3n

3191 P312(00p,1/31/3q)000

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -x,-x+y,-z,-t,-u; y,x,-z,-t,-u; x-y,-y,-z,-t,-u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n

3192 P3112(00p,1/31/3q)000 equivalent group: P312(00p,1/31/3q)000 P3112(00p,1/31/3q).t0.00 P312(00p,1/31/3q).t0.00 P3112(00p,1/31/3q).t0.00 P312(00p,1/31/3q).t0.00

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,1/3+z,t,u; -x+y,-x,2/3+z,t,u; -x,-x+y,-z,-t,-u; y,x,2/3-z,-t,-u; x-y,-y,1/3-z,-t,-u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 00lmn:l=3n 00lmn:2l=3n

3193 P312(00p,1/31/3q).t0.00 equivalent group: P312(00p,1/31/3q).t0.00

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,1/3+t,u; -x+y,-x,z,2/3+t,u; -x,-x+y,-z,-t,-u; y,x,-z,2/3-t,-u; x-y,-y,-z,1/3-t,-u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 00lmn:m=3n 00lmn:2m=3n

3194 P312(p00,0p0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,-z,-u,-t; -x+y,y,-z,-t+u,u; x,x-y,-z,t,t-u;

3195 P3112(p00,0p0)00m equivalent group: P312(p00,0p0)00m

x,y,z,t,u; -y,x-y,1/3+z,-u,t-u; -x+y,-x,2/3+z,-t+u,-t; -y,-x,-z,-u,-t; -x+y,y,2/3-z,-t+u,u; x,x-y,1/3-z,t,t-u;

00l00:l=3n 00l00:2l=3n

3196 P312(-p2p0,-2pp0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,-z,u,t; -x+y,y,-z,t-u,-u; x,x-y,-z,-t,-t+u;

3197 P3112(-p2p0,-2pp0)00m equivalent group: P312(-p2p0,-2pp0)00m

x,y,z,t,u; -y,x-y,1/3+z,-u,t-u; -x+y,-x,2/3+z,-t+u,-t; -y,-x,-z,u,t; -x+y,y,2/3-z,t-u,-u; x,x-y,1/3-z,-t,-t+u;

00l00:l=3n 00l00:2l=3n

3198 P312(-p2p1/3,-2pp2/3)00m

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,-z,u,t; -x+y,y,-z,t-u,-u; x,x-y,-z,-t,-t+u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3199 P321(00p,00q)000

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; y,x,-z,-t,-u; x-y,-y,-z,-t,-u; -x,-x+y,-z,-t,-u;

3200 P321(00p,00q).0t.00 equivalent group: P321(00p,00q).0t.00 P321(00p,00q).t0.00 P321(00p,00q).tt.00 P321(00p,00q).tt.00 P321(00p,00q).t0.00 P321(00p,00q).tt.00 P321(00p,00q).tt.00

x,y,z,t,u; -y,x-y,z,t,1/3+u; -x+y,-x,z,t,2/3+u; y,x,-z,-t,-u; x-y,-y,-z,-t,2/3-u; -x,-x+y,-z,-t,1/3-u;

00lmn:n=3n 00lmn:2n=3n

3201 P3121(00p,00q)000 equivalent group: P3121(00p,00q).0t.00 P3121(00p,00q).0t.00 P3121(00p,00q).t0.00 P3121(00p,00q).tt.00 P3121(00p,00q).tt.00 P3121(00p,00q).t0.00 P3121(00p,00q).tt.00 P3121(00p,00q).tt.00 P321(00p,00q)000 P321(00p,00q).0t.00 P321(00p,00q).0t.00 P321(00p,00q).t0.00 P321(00p,00q).tt.00 P321(00p,00q).tt.00 P321(00p,00q).t0.00 P321(00p,00q).tt.00 P321(00p,00q).tt.00

x,y,z,t,u; -y,x-y,1/3+z,t,u; -x+y,-x,2/3+z,t,u; y,x,-z,-t,-u; x-y,-y,2/3-z,-t,-u; -x,-x+y,1/3-z,-t,-u;

00lmn:l=3n 00lmn:2l=3n

3202 P321(-p2p0,-2pp0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,-u,-t; x-y,-y,-z,-t+u,u; -x,-x+y,-z,t,t-u;

3203 P3121(-p2p0,-2pp0)0m0 equivalent group: P321(-p2p0,-2pp0)0m0

x,y,z,t,u; -y,x-y,1/3+z,-u,t-u; -x+y,-x,2/3+z,-t+u,-t; y,x,-z,-u,-t; x-y,-y,2/3-z,-t+u,u; -x,-x+y,1/3-z,t,t-u;

00l00:l=3n 00l00:2l=3n

3204 P321(p00,0p0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,u,t; x-y,-y,-z,t-u,-u; -x,-x+y,-z,-t,-t+u;

3205 P3121(p00,0p0)0m0 equivalent group: P321(p00,0p0)0m0

x,y,z,t,u; -y,x-y,1/3+z,-u,t-u; -x+y,-x,2/3+z,-t+u,-t; y,x,-z,u,t; x-y,-y,2/3-z,t-u,-u; -x,-x+y,1/3-z,-t,-t+u;

00l00:l=3n 00l00:2l=3n

3206 P321(p01/3,0p2/3)0m0

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,u,t; x-y,-y,-z,t-u,-u; -x,-x+y,-z,-t,-t+u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3207 R3m(00p,00q)00

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,z,t,u; -x+y,y,z,t,u; x,x-y,z,t,u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3208 R3m(00p,00q)0.0s. equivalent group: R3m(00p,00q)0.s0. R3m(00p,00q)0.ss.

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,z,t,1/2+u; -x+y,y,z,t,1/2+u; x,x-y,z,t,1/2+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n -kklmn:n=2n 0klmn:n=2n h0lmn:n=2n

3209 R3c(00p,00q)00 equivalent group: R3c(00p,00q)0.0s. R3c(00p,00q)0.s0. R3c(00p,00q)0.ss.

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; 1/2-y,1/2+x-y,z,t,u; -x+y,1/2-x,z,t,u; 1/2-y,1/2-x,1/2+z,t,u; -x+y,y,1/2+z,t,u; x,1/2+x-y,1/2+z,t,u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n -kklmn:l=2n 0klmn:l=2n h0lmn:l=2n

3210 R3m(p00,0p0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,-u,-t; -x+y,y,z,-t+u,u; x,x-y,z,t,t-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3211 R3c(p00,0p0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; 1/2-y,1/2+x-y,z,-u,t-u; -x+y,1/2-x,z,-t+u,-t; 1/2-y,1/2-x,1/2+z,-u,-t; -x+y,y,1/2+z,-t+u,u; x,1/2+x-y,1/2+z,t,t-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n h-hl-nn:l=2n 0kl0n:l=2n h0lm0:l=2n

3212 R3m(-p2p0,-2pp0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,u,t; -x+y,y,z,t-u,-u; x,x-y,z,-t,-t+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3213 R3c(-p2p0,-2pp0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; 1/2-y,1/2+x-y,z,-u,t-u; -x+y,1/2-x,z,-t+u,-t; 1/2-y,1/2-x,1/2+z,u,t; -x+y,y,1/2+z,t-u,-u; x,1/2+x-y,1/2+z,-t,-t+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n -kklnn:l=2n 0kl-2nn:l=2n h0lm-2m:l=2n

3214 P3m1(00p,00q)000

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,z,t,u; -x+y,y,z,t,u; x,x-y,z,t,u;

3215 P3m1(00p,00q)0.0s.0 equivalent group: P3m1(00p,00q)0.s0.0 P3m1(00p,00q)0.ss.0

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,z,t,1/2+u; -x+y,y,z,t,1/2+u; x,x-y,z,t,1/2+u;

-kklmn:n=2n 0klmn:n=2n h0lmn:n=2n

3216 P3c1(00p,00q)000 equivalent group: P3c1(00p,00q)0.0s.0 P3c1(00p,00q)0.s0.0 P3c1(00p,00q)0.ss.0

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,1/2+z,t,u; -x+y,y,1/2+z,t,u; x,x-y,1/2+z,t,u;

-kklmn:l=2n 0klmn:l=2n h0lmn:l=2n

3217 P3m1(p00,0p0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,-u,-t; -x+y,y,z,-t+u,u; x,x-y,z,t,t-u;

3218 P3c1(p00,0p0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,1/2+z,-u,-t; -x+y,y,1/2+z,-t+u,u; x,x-y,1/2+z,t,t-u;

h-hl-nn:l=2n 0kl0n:l=2n h0lm0:l=2n

3219 P3m1(p01/3,0p2/3)0m0

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,-u,-t; -x+y,y,z,-t+u,u; x,x-y,z,t,t-u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3220 P3c1(p01/3,0p2/3)0?0

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,5/6+z,2/3-u,1/3-t; -x+y,y,5/6+z,2/3-t+u,1/3+u; x,x-y,5/6+z,2/3+t,1/3+t-u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n h-hl-nn:5l-n+5n=6n 0kl0n:5l+0+2n=6n h0lm0:5l+4m+20=6n

3221 P3m1(-p2p0,-2pp0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,u,t; -x+y,y,z,t-u,-u; x,x-y,z,-t,-t+u;

3222 P3c1(-p2p0,-2pp0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,1/2+z,u,t; -x+y,y,1/2+z,t-u,-u; x,x-y,1/2+z,-t,-t+u;

-kklnn:l=2n 0kl-2nn:l=2n h0lm-2m:l=2n

3223 P31m(00p,00q)000

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; y,x,z,t,u; x-y,-y,z,t,u; -x,-x+y,z,t,u;

3224 P31m(00p,00q)00.0s. equivalent group: P31m(00p,00q)00.s0. P31m(00p,00q)00.ss.

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; y,x,z,t,1/2+u; x-y,-y,z,t,1/2+u; -x,-x+y,z,t,1/2+u;

kklmn:n=2n -2kklmn:n=2n h-2hlmn:n=2n

3225 P31c(00p,00q)000 equivalent group: P31c(00p,00q)00.0s. P31c(00p,00q)00.s0. P31c(00p,00q)00.ss.

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; y,x,1/2+z,t,u; x-y,-y,1/2+z,t,u; -x,-x+y,1/2+z,t,u;

kklmn:l=2n -2kklmn:l=2n h-2hlmn:l=2n

3226 P31m(00p,1/31/3q)000

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,z,t,u; -y,-x,z,t,u; -x+y,y,z,t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n

3227 P31m(00p,1/31/3q)00.0s.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,z,t,1/2+u; -y,-x,z,t,1/2+u; -x+y,y,z,t,1/2+u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n h0lmn:n=2n -kklmn:n=2n 0klmn:n=2n

3228 P31m(00p,1/31/3q)00.s0.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,z,1/2+t,u; -y,-x,z,1/2+t,u; -x+y,y,z,1/2+t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n h0lmn:m=2n -kklmn:m=2n 0klmn:m=2n

3229 P31m(00p,1/31/3q)00.ss.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,z,1/2+t,1/2+u; -y,-x,z,1/2+t,1/2+u; -x+y,y,z,1/2+t,1/2+u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n h0lmn:m+n=2n -kklmn:m+n=2n 0klmn:m+n=2n

3230 P31c(00p,1/31/3q)000 equivalent group: P31c(00p,1/31/3q)00.0s. P31c(00p,1/31/3q)00.s0. P31c(00p,1/31/3q)00.ss.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,1/2+z,t,u; -y,-x,1/2+z,t,u; -x+y,y,1/2+z,t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n h0lmn:l=2n -kklmn:l=2n 0klmn:l=2n

3231 P31m(-p2p0,-2pp0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,z,-u,-t; x-y,-y,z,-t+u,u; -x,-x+y,z,t,t-u;

3232 P31c(-p2p0,-2pp0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,1/2+z,-u,-t; x-y,-y,1/2+z,-t+u,u; -x,-x+y,1/2+z,t,t-u;

hhl-nn:l=2n -2kkl0n:l=2n h-2hlm0:l=2n

3233 P31m(-p2p1/3,-2pp2/3)00m

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,z,-u,-t; x-y,-y,z,-t+u,u; -x,-x+y,z,t,t-u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3234 P31c(-p2p1/3,-2pp2/3)00?

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,5/6+z,2/3-u,1/3-t; x-y,-y,5/6+z,2/3-t+u,1/3+u; -x,-x+y,5/6+z,2/3+t,1/3+t-u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n hhl-nn:5l-n+5n=6n -2kkl0n:5l+0+2n=6n h-2hlm0:5l+4m+20=6n

3235 P31m(p00,0p0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,z,u,t; x-y,-y,z,t-u,-u; -x,-x+y,z,-t,-t+u;

3236 P31c(p00,0p0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,1/2+z,u,t; x-y,-y,1/2+z,t-u,-u; -x,-x+y,1/2+z,-t,-t+u;

kklnn:l=2n -2kkl-2nn:l=2n h-2hlm-2m:l=2n

3237 R-3m(00p,00q)00

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; y,x,-z,-t,-u; x-y,-y,-z,-t,-u; -x,-x+y,-z,-t,-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -y,-x,z,t,u; -x+y,y,z,t,u; x,x-y,z,t,u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3238 R-3m(00p,00q)0.0s. equivalent group: R-3m(00p,00q)0.s0. R-3m(00p,00q)0.ss.

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; y,x,-z,-t,1/2-u; x-y,-y,-z,-t,1/2-u; -x,-x+y,-z,-t,1/2-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -y,-x,z,t,1/2+u; -x+y,y,z,t,1/2+u; x,x-y,z,t,1/2+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n -kklmn:n=2n 0klmn:n=2n h0lmn:n=2n

3239 R-3c(00p,00q)00 equivalent group: R-3c(00p,00q)0.0s. R-3c(00p,00q)0.s0. R-3c(00p,00q)0.ss.

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; 1/2-y,1/2+x-y,z,t,u; -x+y,1/2-x,z,t,u; 1/2+y,1/2+x,1/2-z,-t,-u; x-y,-y,1/2-z,-t,-u; -x,1/2-x+y,1/2-z,-t,-u; -x,-y,-z,-t,-u; 1/2+y,1/2-x+y,-z,-t,-u; x-y,1/2+x,-z,-t,-u; 1/2-y,1/2-x,1/2+z,t,u; -x+y,y,1/2+z,t,u; x,1/2+x-y,1/2+z,t,u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n hh000:h+h=2n h-2h000:2h=2n -kklmn:l=2n 0klmn:l=2n h0lmn:l=2n

3240 R-3m(p00,0p0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,u,t; x-y,-y,-z,t-u,-u; -x,-x+y,-z,-t,-t+u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; -y,-x,z,-u,-t; -x+y,y,z,-t+u,u; x,x-y,z,t,t-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3241 R-3c(p00,0p0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,u,t; x-y,-y,-z,t-u,-u; -x,-x+y,-z,-t,-t+u; -x,-y,1/2-z,-t,-u; y,-x+y,1/2-z,u,-t+u; x-y,x,1/2-z,t-u,t; -y,-x,1/2+z,-u,-t; -x+y,y,1/2+z,-t+u,u; x,x-y,1/2+z,t,t-u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n h-hl-nn:l=2n 0kl0n:l=2n h0lm0:l=2n

3242 R-3m(-p2p0,-2pp0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,-u,-t; x-y,-y,-z,-t+u,u; -x,-x+y,-z,t,t-u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; -y,-x,z,u,t; -x+y,y,z,t-u,-u; x,x-y,z,-t,-t+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n

3243 R-3c(-p2p0,-2pp0)0m

(00000;2/31/31/300;1/32/32/300)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; y,x,-z,-u,-t; x-y,-y,-z,-t+u,u; -x,-x+y,-z,t,t-u; -x,-y,1/2-z,-t,-u; y,-x+y,1/2-z,u,-t+u; x-y,x,1/2-z,t-u,t; -y,-x,1/2+z,u,t; -x+y,y,1/2+z,t-u,-u; x,x-y,1/2+z,-t,-t+u;

hklmn:2h+k+l=3n hklmn:h+2k+2l=3n -kklnn:l=2n 0kl-2nn:l=2n h0lm-2m:l=2n

3244 P-31m(00p,00q)000

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,-z,-t,-u; -y,-x,-z,-t,-u; -x+y,y,-z,-t,-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x,-x+y,z,t,u; y,x,z,t,u; x-y,-y,z,t,u;

3245 P-31m(00p,00q)00.0s. equivalent group: P-31m(00p,00q)00.s0. P-31m(00p,00q)00.ss.

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,-z,-t,1/2-u; -y,-x,-z,-t,1/2-u; -x+y,y,-z,-t,1/2-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x,-x+y,z,t,1/2+u; y,x,z,t,1/2+u; x-y,-y,z,t,1/2+u;

h-2hlmn:n=2n kklmn:n=2n -2kklmn:n=2n

3246 P-31c(00p,00q)000 equivalent group: P-31c(00p,00q)00.0s. P-31c(00p,00q)00.s0. P-31c(00p,00q)00.ss.

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x,x-y,1/2-z,-t,-u; -y,-x,1/2-z,-t,-u; -x+y,y,1/2-z,-t,-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x,-x+y,1/2+z,t,u; y,x,1/2+z,t,u; x-y,-y,1/2+z,t,u;

h-2hlmn:l=2n kklmn:l=2n -2kklmn:l=2n

3247 P-31m(00p,1/31/3q)000

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x-y,-y,-z,-t,-u; -x,-x+y,-z,-t,-u; y,x,-z,-t,-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x+y,y,z,t,u; x,x-y,z,t,u; -y,-x,z,t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n

3248 P-31m(00p,1/31/3q)00.0s.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x-y,-y,-z,-t,1/2-u; -x,-x+y,-z,-t,1/2-u; y,x,-z,-t,1/2-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x+y,y,z,t,1/2+u; x,x-y,z,t,1/2+u; -y,-x,z,t,1/2+u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 0klmn:n=2n h0lmn:n=2n -kklmn:n=2n

3249 P-31m(00p,1/31/3q)00.s0.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x-y,-y,-z,1/2-t,-u; -x,-x+y,-z,1/2-t,-u; y,x,-z,1/2-t,-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x+y,y,z,1/2+t,u; x,x-y,z,1/2+t,u; -y,-x,z,1/2+t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 0klmn:m=2n h0lmn:m=2n -kklmn:m=2n

3250 P-31m(00p,1/31/3q)00.ss.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x-y,-y,-z,1/2-t,1/2-u; -x,-x+y,-z,1/2-t,1/2-u; y,x,-z,1/2-t,1/2-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x+y,y,z,1/2+t,1/2+u; x,x-y,z,1/2+t,1/2+u; -y,-x,z,1/2+t,1/2+u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 0klmn:m+n=2n h0lmn:m+n=2n -kklmn:m+n=2n

3251 P-31c(00p,1/31/3q)000 equivalent group: P-31c(00p,1/31/3q)00.0s. P-31c(00p,1/31/3q)00.s0. P-31c(00p,1/31/3q)00.ss.

(00000;1/32/3002/3;2/31/3001/3)

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; x-y,-y,1/2-z,-t,-u; -x,-x+y,1/2-z,-t,-u; y,x,1/2-z,-t,-u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; -x+y,y,1/2+z,t,u; x,x-y,1/2+z,t,u; -y,-x,1/2+z,t,u;

hklmn:h+2k+2n=3n hklmn:2h+k+n=3n 0klmn:l=2n h0lmn:l=2n -kklmn:l=2n

3252 P-31m(2p-p0,pp0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; x,x-y,-z,u,t; -y,-x,-z,t-u,-u; -x+y,y,-z,-t,-t+u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; -x,-x+y,z,-u,-t; y,x,z,-t+u,u; x-y,-y,z,t,t-u;

3253 P-31c(2p-p0,pp0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; x,x-y,-z,u,t; -y,-x,-z,t-u,-u; -x+y,y,-z,-t,-t+u; -x,-y,1/2-z,-t,-u; y,-x+y,1/2-z,u,-t+u; x-y,x,1/2-z,t-u,t; -x,-x+y,1/2+z,-u,-t; y,x,1/2+z,-t+u,u; x-y,-y,1/2+z,t,t-u;

h-2hl-nn:l=2n kkl0n:l=2n -2kklm0:l=2n

3254 P-31m(2p-p1/3,pp2/3)00m

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; x,x-y,-z,u,t; -y,-x,-z,t-u,-u; -x+y,y,-z,-t,-t+u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; -x,-x+y,z,-u,-t; y,x,z,-t+u,u; x-y,-y,z,t,t-u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3255 P-31c(2p-p1/3,pp2/3)00?

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,1/2-u,t-u; -x+y,-x,z,1/2-t+u,1/2-t; x,x-y,1/6-z,5/6+u,1/6+t; -y,-x,1/6-z,5/6+t-u,2/3-u; -x+y,y,1/6-z,1/3-t,2/3-t+u; -x,-y,-z,-t,-u; y,-x+y,-z,1/2+u,-t+u; x-y,x,-z,1/2+t-u,1/2+t; -x,-x+y,5/6+z,1/6-u,5/6-t; y,x,5/6+z,1/6-t+u,1/3+u; x-y,-y,5/6+z,2/3+t,1/3+t-u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n h00nn:n+n=2n h-h0-2nn:2n=2n 0k0m-2m:2m=2n h-2hl-nn:5l-4n+2n=6n kkl0n:5l+0+2n=6n -2kklm0:5l+4m+50=6n

3256 P-31m(0p0,-pp0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; x,x-y,-z,-u,-t; -y,-x,-z,-t+u,u; -x+y,y,-z,t,t-u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; -x,-x+y,z,u,t; y,x,z,t-u,-u; x-y,-y,z,-t,-t+u;

3257 P-31c(0p0,-pp0)00m

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; x,x-y,1/2-z,-u,-t; -y,-x,1/2-z,-t+u,u; -x+y,y,1/2-z,t,t-u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; -x,-x+y,1/2+z,u,t; y,x,1/2+z,t-u,-u; x-y,-y,1/2+z,-t,-t+u;

h-2hlnn:l=2n kkl-2nn:l=2n -2kklm-2m:l=2n

3258 P-3m1(00p,00q)000

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,z,t,u; -x+y,y,z,t,u; x,x-y,z,t,u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; y,x,-z,-t,-u; x-y,-y,-z,-t,-u; -x,-x+y,-z,-t,-u;

3259 P-3m1(00p,00q)0.0s.0 equivalent group: P-3m1(00p,00q)0.s0.0 P-3m1(00p,00q)0.ss.0

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,z,t,1/2+u; -x+y,y,z,t,1/2+u; x,x-y,z,t,1/2+u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; y,x,-z,-t,1/2-u; x-y,-y,-z,-t,1/2-u; -x,-x+y,-z,-t,1/2-u;

-kklmn:n=2n 0klmn:n=2n h0lmn:n=2n

3260 P-3c1(00p,00q)000 equivalent group: P-3c1(00p,00q)0.0s.0 P-3c1(00p,00q)0.s0.0 P-3c1(00p,00q)0.ss.0

x,y,z,t,u; -y,x-y,z,t,u; -x+y,-x,z,t,u; -y,-x,1/2+z,t,u; -x+y,y,1/2+z,t,u; x,x-y,1/2+z,t,u; -x,-y,-z,-t,-u; y,-x+y,-z,-t,-u; x-y,x,-z,-t,-u; y,x,1/2-z,-t,-u; x-y,-y,1/2-z,-t,-u; -x,-x+y,1/2-z,-t,-u;

-kklmn:l=2n 0klmn:l=2n h0lmn:l=2n

3261 P-3m1(-p2p0,-2pp0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,u,t; -x+y,y,z,t-u,-u; x,x-y,z,-t,-t+u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; y,x,-z,-u,-t; x-y,-y,-z,-t+u,u; -x,-x+y,-z,t,t-u;

3262 P-3c1(-p2p0,-2pp0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,1/2+z,u,t; -x+y,y,1/2+z,t-u,-u; x,x-y,1/2+z,-t,-t+u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; y,x,1/2-z,-u,-t; x-y,-y,1/2-z,-t+u,u; -x,-x+y,1/2-z,t,t-u;

-kklnn:l=2n 0kl-2nn:l=2n h0lm-2m:l=2n

3263 P-3m1(p00,0p0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,-u,-t; -x+y,y,z,-t+u,u; x,x-y,z,t,t-u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; y,x,-z,u,t; x-y,-y,-z,t-u,-u; -x,-x+y,-z,-t,-t+u;

3264 P-3c1(p00,0p0)0m0

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,1/2+z,-u,-t; -x+y,y,1/2+z,-t+u,u; x,x-y,1/2+z,t,t-u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; y,x,1/2-z,u,t; x-y,-y,1/2-z,t-u,-u; -x,-x+y,1/2-z,-t,-t+u;

h-hl-nn:l=2n 0kl0n:l=2n h0lm0:l=2n

3265 P-3m1(p01/3,0p2/3)0m0

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,z,-u,-t; -x+y,y,z,-t+u,u; x,x-y,z,t,t-u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; y,x,-z,u,t; x-y,-y,-z,t-u,-u; -x,-x+y,-z,-t,-t+u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n

3266 P-3c1(p01/3,0p2/3)0?0

(00000;001/32/31/3;002/31/32/3)

x,y,z,t,u; -y,x-y,z,-u,t-u; -x+y,-x,z,-t+u,-t; -y,-x,5/6+z,2/3-u,1/3-t; -x+y,y,5/6+z,2/3-t+u,1/3+u; x,x-y,5/6+z,2/3+t,1/3+t-u; -x,-y,-z,-t,-u; y,-x+y,-z,u,-t+u; x-y,x,-z,t-u,t; y,x,1/6-z,1/3+u,2/3+t; x-y,-y,1/6-z,1/3+t-u,2/3-u; -x,-x+y,1/6-z,1/3-t,2/3-t+u;

hklmn:l+2m+n=3n hklmn:2l+m+2n=3n h-hl-nn:5l-n+5n=6n 0kl0n:5l+0+2n=6n h0lm0:5l+4m+20=6n hh0nn:n+n=2n h-2h0m-2m:2m=2n