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The Group p4m

Generators: t1, R4, Mm
Relations: t2 = R4 t1 R4-1, R42 = e, Mm2 = e
Cell diagram: [Image]

Table: Six homomorphisms from p4m
type P(k) = -1 wallpaper type of kernel group, with remarks
p4m [Image] none p4m, same as the extended group
p4m'm' [Image] Mm p4 = {t1, R4}
p4'm'm [Image] R4 cmm = {t1, Mm, R42}
p4'mm' [Image] R4 and Mm pmm = {t1, R4 Mm, R42}
p'c4mm t1 p4m = {t12, R4, Mm}
  t1 and R4 same as above, i(R)=t1 R
p'c4gm t1 and Mm p4g = {t12, R4, t1 Mm}
  t1, R4, and Mm same as above, i(R) = t1 R

[Next] The Groups p3, p31m, p3m1, p6, and p6m
[Skip] Ways to Visualize Wallpaper Functions
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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