[Prev][Next][Skip][Up][UpUp][Top] VW - CVM 1.1 [Bib][Respond][Find][Help]


The Group cmm

Generators: d, Mx, R
Relations: d' = Mx d Mx-1, t1 = d'd-1, t2 = d'd,
R2 = e, Mx2 = e
Cell diagram: [Image]


Table: Six homomorphisms from cmm
type P(k) = -1 wallpaper type of kernel group, with remarks
cmm [Image] none cmm, same as the extended group
cmm' [Image] R cm = {t1, Mx}
  R and Mx same as above, i(M) = R Mx
cm'm' Mx p2 = {d, d', R}
p'cmm [Image] d pmm = {t1, t2, Mx, R}; cell doubled
p'cmg [Image] d and R pmg = {t1, t2, Mx, d R}; cell doubled
  d, R and Mx same as above, i(M) = R Mx
p'cgg d and Mx pgg = {d Mx (= L), R}; cell doubled


[Next] The Group p4
[Skip] Ways to Visualize Wallpaper Functions
[Up] Why there are 63 Types
[UpUp] The Algebra of Wallpapers
[Prev] The Group cm
[Bib][Respond]
[Find][Help] 

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