How to draw stick trefoil knot

Question

http://commons.wikimedia.org/wiki/File:Stick_number_trefoil.png I am interested in plotting the stick trefoil knot. I don't know where to start. I am looking for equations or co-ordinates of vertices, so that i can plot it. Thanks

Answer 1

Let's first distribute same labels:

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Let the $C$ lie at $(1,0)$, $F$ at $a(1,0)$, $A$ at $(\cos(2\pi/3),-\sin(2\pi/3))$ and $D$ at $a(\cos(2\pi/3),-\sin(2\pi/3))$. You need to check whether $|CD|=|AF|$ and this is: $$ |(1-a\cos(2\pi/3),-a\sin(2\pi/3))|=|(a-\cos(2\pi/3),-\sin(2\pi/3))|\\ \sqrt{(1-a\cos(2\pi/3))^2+a^2\sin^2(2\pi/3)}=\sqrt{(a-\cos(2\pi/3))^2+\sin(2\pi/3)}\\ 1-2a\cos(2\pi/3) +1 = a^2+2a\cos(2\pi/3)+1\\ a^2+2a-1=0\\ a=\sqrt{2}-1 $$

ok I skipped ambiguities with the squares and the roots of the last equation... For your information, these graphs are called Unit distance graphs.