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The Group p4g


	Generators:		R₄, M_e

	Relations:		t₂ = R₄ t₁ R₄^-1 = (R₄ M_e)², R₄⁴ = e, M_e² = e

	Cell diagram:

**Table:** Four homomorphisms from p4g
type	P(k) = -1	wallpaper type of kernel group, with remarks
p4g	none	p4g, same as the extended group
p4'g'm	R₄	cmm = {t₁, M_e, R₄²}
p4'gm'	R₄ and M_e	pgg = {t₁, R₄², R₄ M_e}
p4g'm'	M_e	p4 = {t₁, R₄}

	The Group p4m
	Ways to Visualize Wallpaper Functions
	Why there are 63 Types
	The Algebra of Wallpapers
	The Group p4

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