# Untitled Course对称组和墙纸

+=
+=

+
=
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*增加两个旋转将始终产生 （或身份）。 *添加两个反射将始终 （或身份）。 *以相反的顺序添加相同的两个对称结果。 *添加身份

1. Adding two symmetries/integers always gives another symmetry/integer:
+=
12+7=19
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++=++
4+2+5=4+2+5
Continue
3. Every symmetry/integer has an inverse, another symmetry/integer which, when added, gives the identity:
+=
4+–4=0
Continue

CCl 4分子（左）和腺病毒（右）的特性由它们的对称性决定。

## 墙纸组

Group 1 – P1

Only translations div img(src="/content/transformations/images/wallpapers/p2.svg" width=360, height=240) p.caption Group 2 – P2 Rotations of order 2, translations div img(src="/content/transformations/images/wallpapers/p3.svg" width=360, height=240) p.caption Group 3 – P3 Rotations of order 3 (120°), translations div img(src="/content/transformations/images/wallpapers/p4.svg" width=360, height=240) p.caption Group 4 – P4 Four rotations of order 2 (180°), translations div img(src="/content/transformations/images/wallpapers/p6.svg" width=360, height=240) p.caption Group 5 – P6 Rotations of order 2, 3 and 6 (60°), translations div img(src="/content/transformations/images/wallpapers/pm.svg" width=360, height=240) p.caption Group 6 – PM Parallel axes of reflection, translations div img(src="/content/transformations/images/wallpapers/pmm.svg" width=360, height=240) p.caption Group 7 – PMM Perpendicular reflections, rotations of order 2, translations div img(src="/content/transformations/images/wallpapers/p4m.svg" width=360, height=240) p.caption Group 8 – P4M Rotations (ord 2 + 4), reflections, glide reflections, translations div img(src="/content/transformations/images/wallpapers/p6m.svg" width=360, height=240) p.caption Group 9 – P6M Rotations (ord 2 + 6), reflections, glide reflections, translations div img(src="/content/transformations/images/wallpapers/p3m1.svg" width=360, height=240) p.caption Group 10 – P3M1 Rotations of order 3, reflections, glide reflections, translations div img(src="/content/transformations/images/wallpapers/p31m.svg" width=360, height=240) p.caption Group 11 – P31M Rotations of order 3, reflections, glide reflections, translations div img(src="/content/transformations/images/wallpapers/p4g.svg" width=360, height=240) p.caption Group 12 – P4G Rotations (ord 2 + 4), reflections, glide reflections, translations div img(src="/content/transformations/images/wallpapers/cmm.svg" width=360, height=240) p.caption Group 13 – CMM Perpendicular reflections, rotations of order 2, translations div img(src="/content/transformations/images/wallpapers/pmg.svg" width=360, height=240) p.caption Group 14 – PMG Reflections, glide reflections, rotations of order 2, translations div img(src="/content/transformations/images/wallpapers/pg.svg" width=360, height=240) p.caption Group 15 – PG Parallel glide reflections, translations div img(src="/content/transformations/images/wallpapers/cm.svg" width=360, height=240) p.caption Group 16 – CM Reflections, glide reflections, translations div img(src="/content/transformations/images/wallpapers/pgg.svg" width=360, height=240) p.caption Group 17 – PGG Perpendicular glide reflections, rotations of order 2, translations

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