Let's continue to consider tessellations, tiles and tilings.
Although the original three plane tessellation are somewhat mundane they do pose a demanding challenge in terms of 'elegant' LOGO procedures.
This month consider the eight semi-regular tessellations, which geometrically are more stimulating and are shown below along with their respective Schläfli symbols.
Look carefully at each diagram in turn. Can you see the purpose the symbols serve?
You may like to research these symbols further. The symbols are used in two and in three dimensions in classifying the regular and semi-regular solids and you can see an account of this in this NRICH article by Warwick Evans.
Construct some elegant procedures to replicate these very important geometric ideas.
For beginners, just start with drawing regular polygons; equilateral triangles, squares, pentagons, hexagons etc. It's very easy. Here is a reminder of some of the PRIMITIVES (the commands) needed to start drawing:
| FD forward | BK backward |
| LT left | RT right |
| PU pen up | PD pen down |
| HT hide turtle | ST show turtle |
| CS clear screen | CT clear text |
Here is an example of the use of REPEAT. Try it!
REPEAT 5 [FD 30 RT 72]
Now try REPEAT 3 and REPEAT 4 etc and vary the distances and the angles. Away you go!