The Perko Praxinoscope and the Shrikhande Graph

As I mentioned in my previous update, I fixed the design for the Perko knots on the pegs, and made a decision on designing the Shrikhande graph so that it looked like the Rook’s graph. Well I sent them off to Shapeways and was overjoyed when I received them a week or so later: they were perfect!

First, the pegs for the Perko knots fit very well on the Praxinoscope. Also, the knots were still attached to the pegs when I received them, which is nice! Here they are laid out:

And here they are on the actual praxinoscope:

And here’s a video of it in action! Though we only have ten frames, you can still see the knot morphing as the praxinoscope spins.

On top of the Perko knot project working out really nicely, the Shrikhande graph came out perfectly! Here is a picture of it:

I think this fulfills its purpose – if you hold this print and the $4 \times 4$ Rook’s graph together, then you can really see the similarities and differences between the two.

In terms of plans for the future, I am hoping to 3D print a book embedding of a graph that really looks like a book! Here’s a sneak preview of the book design:

Jonathan Gerhard

I am a first-year PhD student in mathematics at the University of Michigan and I got my BS in mathematics in 2017 from James Madison University. I started this blog because I love math!

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