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The k-vector types of layers group p -6 m 2 (No. 78)

(Table for arithmetic crystal class -6m2p)

p-6m2 (No. 78)

Reciprocal plane group (p31m)* (No. 15)

Brillouin zone


k-vector descriptionPlane-group description
Label(1)Coefficients Little layer
co-group		Wyckoff PositionCoordinates
GM0,0-6m21a3.m0,0
K1/3,1/3-6..2b3..2/3,1/3
M1/2,0 exmm23c..m1/2,0
SMu,0 exmm23c..mx,0 : 0 < x < 1/2
SN0,u exmm23c..mx,x : 0 < x < 1/2
SN~SN1=[M AA]3c..mx,0 : 1/2 < x < 1
M+SM+SN1=[GM AA]3c..mx,0 : 0 < x < 1
LDu,u exm..6d1x,x/2 : 0 < x < 2/3
T1/2-u,2u exm..6d1x+1/2,2x : 0 < x < 1/6
B=[GM K M]u,v exm..6d1x,y : 0 < y < x/2, 2x-1 < y
BB=[GM K M2]v,u exm..6d1x,y : x/2 < y < x, y < 1-x
BB~BB1=[M K AA]6d1x,y : 0 < y < 1-x, y < 2x-1
LD+T+B+BB1=[GM K AA]6d1x,y : 0 < y < x/2; y < 1-x


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. The reciprocal bases:
2. The k-vector: kx ky

(*)In this case the primitive and conventional bases coincide



(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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