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Schlafli Tessellations

Age 11 to 18 Challenge Level:

Although the three regular tessellation (using squares, triangles and hexagons) are well known, they do pose a demanding challenge in terms of 'elegant' LOGO procedures.

This problem considers the eight semi-regular tessellations, which geometrically are more stimulating and are shown below, along with their respective Schlafli symbols.

Look carefully at each diagram in turn. What is the meaning of the symbols?

The symbols are used in two and in three dimensions in classifying the regular and semi-regular solids. You can see an account of this in this NRICH article by Warwick Evans.

Can you construct some elegant procedures to replicate these images?