VW - CVM 1.1

The Group cmm

	Generators:		d, Mx, R
	Relations:		d' = Mx d Mx-1, t1 = d'd-1, t2 = d'd, R2 = e, Mx2 = e
	Cell diagram:

Table: Six homomorphisms from cmm

type	P(k) = -1	wallpaper type of kernel group, with remarks
cmm	none	cmm, same as the extended group
cmm'	R	cm = {t1, Mx}
	R and Mx	same as above, i(M) = R Mx
cm'm'	Mx	p2 = {d, d', R}
p'cmm	d	pmm = {t1, t2, Mx, R}; cell doubled
p'cmg	d and R	pmg = {t1, t2, Mx, d R}; cell doubled
	d, R and Mx	same as above, i(M) = R Mx
p'cgg	d and Mx	pgg = {d Mx (= L), R}; cell doubled

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