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The k-vector types of layers group c m 2 m (No. 35)

(Table for arithmetic crystal class m2mc) a > b

cm2m (No. 35), cm2e (No. 36)

Reciprocal plane group (c1m1)* (No. 5) a* < b*

Brillouin zone


k-vector descriptionPlane-group description
Label(1)Primitive basis Conventional basisLittle layer co-groupWyckoff PositionCoordinates
GM0,0 ex0,0m2m2a.m.0,0
Y1/2,1/2 ex1,0m2m2a.m.1/2,0
Y~Y22a.m.0,1/2
DT-u,u ex0,2um2m2a.m.0,y : 0 < y <= dt0
DAu,-u ex0,-2um2m2a.m.0,y : dt2=-dt0 <= y <0
F1/2-u,1/2+u ex1,2um2m2a.m.1/2,y : 0 < y < f0=1/2-dt0
FA~DT1=[DT0 Y2]2a.m.0,y : dt0 < y <1/2
FA1/2+u,1/2-u ex1,-2um2m2a.m.1/2,y : f2=-f0 < y < 0
F~DA1=[DT2 Y4]2a.m.0,y : -1/2 < y < dt2=-dt0
GM+Y2+DT+DT1+DA+DA12a.m.0,y : -1/2 < y <= 1/2
S0,1/2 ex1/2,1/2..m4b11/4,1/4
SMu,u ex2u,0..m4b1x,0 : 0 < x < 1/2
Pu,v exu+v,-u+v..m4b1x,y : [GM Y F0 DT0]
P~P1=[GM J2 J4 Y]4b11/2,y : 0 < x < 1/2, 0 < y < 1/4
PAv,u exv+u,-v+u ..m4b1x,y : [GM Y F2 DT2]
PA~PA1=[GM V2 V4 Y]4b1x,y : 0 < x < 1/2; -1/4 < y < 0
P1+PA1+SM+S4b1x,y : 0 < x < 1/2, -1/4 < y < 1/4

The representation domain of Litvin & Wike is different from the asymmetic unit

Flagpoles: [J2 Y2] 0,y: 1/4 < y < 1/2 and [V2 Y4] 0,y: -1/2 < y < -1/4



(Table for arithmetic crystal class m2mc) a < b

cm2m (No. 35), cm2e (No. 36)

Reciprocal plane group (c1m1)* (No. 5) a* > b*

Brillouin zone


k-vector descriptionPlane-group description
Label(1)Primitive basis Conventional basisLittle layer co-groupWyckoff PositionCoordinates
GM0,0 ex0,0m2m2a.m.0,0
Y1/2,1/2 ex0,1m2m2a.m.0,1/2
DT-u,u ex0,2um2m2a.m.0,y : 0 < y < 1/2
DAu,-u ex0,-2um2m2a.m.0,y : -1/2 < y < 0
GM+Y+DT+DA2a.m.0,y : -1/2 < y <= 1/2
S0,1/2 ex1/2,1/2..m4b11/4,1/4
SMu,u ex2u,0..m4b1x,0 : 0 < x <= sm0
Cu-1/2,u+1/2 ex2u,1..m4b1x,1/2 : 0 < x < c0=1/2-sm0
C~SM1=[SM0 Y2]4b1x,0 : sm0 < x < 1/2
Pu,v exu+v,-u+v..m4b1x,y : [GM Y C0 SM0]
P~P1=[GM J2 J4 Y2]4b1x,y : 0 < x < 1/2; 0 < y < 1/4
PAv,u exv+u,-v+u ..m4b1x,y : [GM SM0 C2 Y4]
PA~PA1=[GM V2 V4 Y2]4b1x,y : 0 < x < 1/2, -1/4 < y < 0
P1+PA1+SM+SM1+S4b1x,y : 0 < x < 1/2, -1/4 < y < 1/4


Flagpoles: [J2 Y] 0,y: 1/4 < y < 1/2 and [V2 Y4] 0,y: -1/2 < y < -1/4

The representation domain of Litvin & Wike is different from the asymmetic unit



k-vector identification tool

If you want to identify a k-vector you have to introduce:
1. Select the lattice parameters
2. The reciprocal bases:
3. The k-vector: kx ky



(1)Litvin, D. B. & Wike, T. R. (1991). Character Tables and Compatibility Relations of The Eighty Layer Groups and Seventeen Plane Groups. Plenum Press, New York.



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