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Crystals in Flatland

How would molecules come together and arrange to form crystals (including those of 'snowflakes') in Flatland, a flat world of flat creatures made up of flat molecules?

And what could this teach us about crystals--and the arrangements of molecules in them--in our 3-D world?

Two-dimensional crystals (a simplified version of typical 3-dimensional crystals) can be formed in 17 different ways (called 2-dimensional space groups, or plane/planar groups, or wallpaper groups). At the bottom, you will find links to figures illustrating these different arrangements (ignoring hand coloring), with their space group names on the immediate right. As you notice, symmetry is important in crystal formation. (More on symmetry to follow soon.)

Oblique plane groups

p1 p2

Rectangular plane groups

pm pg cm p2mm p2mg p2gg c2mm

Square plane groups

p4 p4mm p4gm

Hexagonal plane groups

p3 p3m1 p31m
p6 p6mm