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The Group pmg


	Generators:		t₁, L_v, A

	Relations:		A² = 0, L_v² = t₂, L_v A = R_c

	Cell diagram:

**Table:** Six homomorphisms from *pmg*
type	P(k) = -1	wallpaper type of kernel group, with remarks
pmg	none	pmg, same as the extended group
p'_bmg	t₁	pmg = {t₁², L_v, A}
	t₁ and L_v	same as above, i(L_v) = L_v t₁
pmg'	L_v	pm = {t₁, L_v², A}; R negative
pm'g	A	pg = {t₁, L_v}; R negative
p'_bgg	t₁ and A	pgg = {t₁², L_v, t₁ A}; doubled cell
	t₁, L_v and A	same as above, i(L_v) = L_v t₁
pm'g'	L_v and A	p2 = {t₁, L_v², L_v A}; R positive

	The Group pgg
	Ways to Visualize Wallpaper Functions
	Why there are 63 Types
	The Algebra of Wallpapers
	The Group pmm

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