Wallpaper lattice confusion

I got home from work last night to discover the decorator still hard at work, putting up the ‘feature’ wallpaper on one fairly small section of wall. He said he’d been struggling for the last hour trying to find the repeat in the pattern. It’s a dark paper, with detailed but low-contrast outlines of flowers in it. Being an expert in this, having done first-year crystallography, I looked at it very carefully. Little wonder the poor guy was struggling. The label on the roll said it repeated every 32 cm.  It didn’t.  It nearly repeated every 32 cm, but there were some subtle differences. The repeat length was actually 64 cm. Once we’d got this sorted, the rest was fairly easy. In crystollagraphic language, we have a rectangular lattice, with lattice constant 64 cm vertically and about 50 cm horizontally (the width of the roll).  The motif has no symmetry at all – i.e. the end result simply has translational symmetry. That’s a p1 wallpaper group.


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