CHAPTER 6 TWO-COLORED WALLPAPER PATTERNS 6.0 ...
CHAPTER 6 TWO-COLORED WALLPAPER PATTERNS 6.0 ...
CHAPTER 6 TWO-COLORED WALLPAPER PATTERNS 6.0 ...
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pg pg′ p b<br />
′ 1g<br />
P P P P P R R R R R P R P R P<br />
Fig. 6.14<br />
In these symmetry plans glide reflection vectors are not shown<br />
for the sake of simplicity, but you must indicate them in your work!<br />
6.3 pm types (pm, pm′ , p b<br />
′ 1m, p′ m, p b<br />
′ g, c′ m)<br />
6.3.1 Upgrading the glide reflection to reflection. Employing an<br />
old idea from 2.7.2 -- where we viewed a pma2 pattern as ‘half’ of a<br />
pmm2 pattern -- in the opposite direction, we are now ‘doubling’<br />
the three pg-like patterns in figures 6.4, 6.9, and 6.11 into pm-like<br />
patterns by ‘fattening’ the glide reflections into reflections; that<br />
is, we reflect the pattern across every glide reflection axis without<br />
gliding the image. This process is bound to produce six two-colored<br />
pm-like patterns having reflection in one direction: indeed as we<br />
reflect across the glide reflection axes we have the option of a<br />
color effect either opposite to or same as that of the glide<br />
reflection (see also 6.3.2 and 6.3.5), so we end up with three × two =<br />
six pm types. We illustrate the process in the following six figures,<br />
indicating in each case the ‘original’ pg-like pattern and providing<br />
the name for the ‘new’ pm-like pattern. Make sure you can<br />
rediscover the old pg-like pattern inside the richer structure of the<br />
new pattern; there is more than mere nostalgia in our call: the old<br />
glide reflection is alive and well, ‘hidden’ under the new reflection<br />
and ready to play an important role in the classification process!