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There's an easy proof of this: you can colour the vertices red and blue so that no vertices joined by an edge are the same colour, and there are an odd number of vertices.
So any lap visiting each vertex once has to end on a different colour to the start.
Here's an image showing the colouring property, by David Eppstein. If you start on blue, you have to finish on red, and vice versa.

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Another one. Here, flocks of arrowheads are tracing out the Herschel graph.
The Herschel graph is something I keep returning to, because our building is named after its inventor.

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Behold, the squircle-oid!
This is the shape defined by the equation
\[ \left(\frac{x}{2}\right)^4 + y^4 + z^4 \leq 1 \]
I made it as part of a set of props for explaining Lᵖ norms. p=2 gives an ellipsoid, and in the limit p → ∞ you get a cuboid.

Here's a closeup of the handwriting one. I wandered round the department knocking on doors, asking people to write some mathematical notation. It was fascinating seeing the different symbols and conventions used in different disciplines.
What can you spot in this snippet?

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Art* is going on walls!
On the right is one of the Truchet pieces I shared above, and the other is made up of handwriting samples I gathered from colleagues. It feels good to finally put something out with this!

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Doing some artistic thinking because I've got to fill a lot of picture frames in the department in a hurry.
Ignoring the colours, which ones do you like the most?
No image descriptions because these are all pretty abstract!

Identify the error correcting code. These cards came with my daughter's new toy

When I stack them on top of each other, this is what it looks like. What do you notice?

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Your idiot colleagues: store whiteboard pens on end to get all the ink out.
You, an intellectual: store them flat to make sure the solvent mixes properly.
Me, a bona fide genius:

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