VW - CVM 1.1

The Group p4m

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

Table: Six homomorphisms from p4m

type	P(k) = -1	wallpaper type of kernel group, with remarks
p4m	none	p4m, same as the extended group
p4m'm'	Mm	p4 = {t1, R4}
p4'm'm	R4	cmm = {t1, Mm, R42}
p4'mm'	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

The Groups p3, p31m, p3m1, p6, and p6m Ways to Visualize Wallpaper Functions Why there are 63 Types The Algebra of Wallpapers The Group p4g