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The Group pm

	Generators:		t1,t2, M
	Relations:		M2 = 0
	Cell diagram:

Table: Six homomorphisms from pm

type	P(k) = -1	wallpaper type of kernel group, with remarks
pm	none	pm, same as the extended group
pm'	M	p1
p'b1m	t1	pm = {t12, t2, M}
p'bm	t2	pm = {t1, t22, M}; new negating mirror
	M and t2	same as above, i(M) = M t2
p'bg	t1 and M	pg = {t12, t2, t1 M}; doubled cell
	t2	not a new type, interchange t1 and t2
c'm	t1 and t2	cm = {t1 t2, t1 t2-1, M}; doubled cell
	M, t1 and t2	same as above, i(M) = M t2

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