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'LOGO Challenge 8 - Rhombi' printed from http://nrich.maths.org/

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Explore :

TO RHOMB :X
REPEAT 2 [ FD :X RT 45 FD :X RT 135]
END

 

TO PAT :X
REPEAT 8 [RHOMB :X LT 45]
END

Pattern 1
How about exploring overlaying the patterns produced. Pattern 2
Or 'exploding' the patterns Pattern 3
Or both! Pattern 4

The invitation for you is to explore further this infrequently met family of shapes.

You might like to start by expanding on the procedures above.