Trigonal Superspace Groups

copyright (c) Jul. 1999 by Akiji Yamamoto 668 R3(00p)0

(0000;2/31/31/30;1/32/32/30)

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

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

669 R3(00p)t equivalent group: R3(00p)t

(0000;2/31/31/30;1/32/32/30)

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

hklm:2h+k+l=3n hklm:h+2k+2l=3n 00lm:m=3n 00lm:2m=3n

670 P3(00p)0

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

671 P3(00p)t equivalent group: P3(00p)t

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

00lm:m=3n 00lm:2m=3n

672 P31(00p)0 equivalent group: P31(00p)t P31(00p)t P3(00p)0 P3(00p)t P3(00p)t

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

00lm:l=3n 00lm:2l=3n

673 P3(1/31/3p)0

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n

674 P31(1/31/3p)0 equivalent group: P3(1/31/3p)0

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n 00lm:l=3n 00lm:2l=3n

675 R-3(00p)0

(0000;2/31/31/30;1/32/32/30)

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

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

676 P-3(00p)0

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

677 P-3(1/31/3p)0

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n

678 R32(00p)00

(0000;2/31/31/30;1/32/32/30)

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

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

679 R32(00p)t0 equivalent group: R32(00p)t0

(0000;2/31/31/30;1/32/32/30)

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

hklm:2h+k+l=3n hklm:h+2k+2l=3n 00lm:m=3n 00lm:2m=3n

680 P312(00p)000

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

681 P312(00p)t00 equivalent group: P312(00p)t00

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

00lm:m=3n 00lm:2m=3n

682 P3112(00p)000 equivalent group: P3112(00p)t00 P3112(00p)t00 P312(00p)000 P312(00p)t00 P312(00p)t00

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

00lm:l=3n 00lm:2l=3n

683 P312(1/31/3p)000

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n

684 P3112(1/31/3p)000 equivalent group: P312(1/31/3p)000

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n 00lm:l=3n 00lm:2l=3n

685 P321(00p)000

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

686 P321(00p)t00 equivalent group: P321(00p)t00

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

00lm:m=3n 00lm:2m=3n

687 P3121(00p)000 equivalent group: P3121(00p)t00 P3121(00p)t00 P321(00p)000 P321(00p)t00 P321(00p)t00

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

00lm:l=3n 00lm:2l=3n

688 R3m(00p)00

(0000;2/31/31/30;1/32/32/30)

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

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

689 R3m(00p)0s

(0000;2/31/31/30;1/32/32/30)

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

hklm:2h+k+l=3n hklm:h+2k+2l=3n -kklm:m=2n 0klm:m=2n h0lm:m=2n

690 R3c(00p)00 equivalent group: R3c(00p)0s

(0000;2/31/31/30;1/32/32/30)

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

hklm:2h+k+l=3n hklm:h+2k+2l=3n -kklm:l=2n 0klm:l=2n h0lm:l=2n

691 P3m1(00p)000

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

692 P3m1(00p)0s0

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

-kklm:m=2n 0klm:m=2n h0lm:m=2n

693 P3c1(00p)000 equivalent group: P3c1(00p)0s0

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

-kklm:l=2n 0klm:l=2n h0lm:l=2n

694 P31m(00p)000

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

695 P31m(00p)00s

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

kklm:m=2n -2kklm:m=2n h-2hlm:m=2n

696 P31c(00p)000 equivalent group: P31c(00p)00s

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

kklm:l=2n -2kklm:l=2n h-2hlm:l=2n

697 P31m(1/31/3p)000

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n

698 P31m(1/31/3p)00s

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n h0lm:m=2n -kklm:m=2n 0klm:m=2n

699 P31c(1/31/3p)000 equivalent group: P31c(1/31/3p)00s

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n h0lm:l=2n -kklm:l=2n 0klm:l=2n

700 R-3m(00p)00

(0000;2/31/31/30;1/32/32/30)

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

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

701 R-3m(00p)0s

(0000;2/31/31/30;1/32/32/30)

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

hklm:2h+k+l=3n hklm:h+2k+2l=3n -kklm:m=2n 0klm:m=2n h0lm:m=2n

702 R-3c(00p)00 equivalent group: R-3c(00p)0s

(0000;2/31/31/30;1/32/32/30)

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

hklm:2h+k+l=3n hklm:h+2k+2l=3n hh00:h+h=2n h-2h00:2h=2n -kklm:l=2n 0klm:l=2n h0lm:l=2n

703 P-31m(00p)000

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

704 P-31m(00p)00s

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

h-2hlm:m=2n kklm:m=2n -2kklm:m=2n

705 P-31c(00p)000 equivalent group: P-31c(00p)00s

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

h-2hlm:l=2n kklm:l=2n -2kklm:l=2n

706 P-31m(1/31/3p)000

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n

707 P-31m(1/31/3p)00s

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n 0klm:m=2n h0lm:m=2n -kklm:m=2n

708 P-31c(1/31/3p)000 equivalent group: P-31c(1/31/3p)00s

(0000;1/32/302/3;2/31/301/3)

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

hklm:h+2k+2m=3n hklm:2h+k+m=3n 0klm:l=2n h0lm:l=2n -kklm:l=2n

709 P-3m1(00p)000

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

710 P-3m1(00p)0s0

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

-kklm:m=2n 0klm:m=2n h0lm:m=2n

711 P-3c1(00p)000 equivalent group: P-3c1(00p)0s0

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

-kklm:l=2n 0klm:l=2n h0lm:l=2n