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Functions having no Positive Mirrors or Rotations

Table: Symmetry types in rectangular cell without mirrors or rotations
type G E Recipe for this type and remarks
pg' [Image] p1 pg n odd with cos(mY) and n even with sin(mY);
L negative
pg [Image] pg pg n even with cos(mY) and n odd with sin(mY);
L positive (M+ h+ or M- h-)
p'bg [Image] pg pm n odd with sin(mY);
L positive, h, M negative
p'b1g [Image] pg pg pg requirements with m odd;
L positive, v, B negative
p'cg [Image] pg cm pg requirements with n + m odd;
L positive, v, A negative
pm'g [Image] pg pmg n even with sin(nX) cos(mY) terms
n odd with cos(nX) sin(mY) terms;
Av and R negative
pgg' [Image] pg pgg n + m even with sin(nX) cos(mY) terms
n + m odd with cos(nX) sin(mY) terms;
Bv and R negative


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Communications in Visual Mathematics, vol 1, no 1, August 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: 08 Jul 1998 --- Last modified: 18 Aug 1998 23:59:59
Comments to: CVM@maa.org