现代无机化学进展课件参考文献2-tiling.pdf

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Nets and Tiling Michael O'Keeffe Introduction to tiling theory

and its lication to crystal nets

Start with tiling in two dimensions.

Surface of sphere and plane

Sphere is two-dimensional. We require only two

coordinates to specify position on the surface

of a sphere:

The coordinates of

Changchun 43.9 N, 234.8 W

Tempe 33.4 N, 121.9 W

As far as we are concerned

Tilings in two dimensions are edge-to-edge

(each edge is common to just two tiles)

In three dimensions face-to-face

(each face common to just two tiles) Three different embeddings of the same abstract tiling

brick wall honeycomb herringbone c2mm p 6mm p2gg Again, two embeddings of the same abstract tiling double brick Cairo tiling

Both h e same symmetry, p 4gm . The Cairo conformation

is the minimum density for equal edges.

Recal

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