George Hart wrote:

But I must say that the SCD design seems to me to convey the same ideas while being so much simpler and pleasantly convex.

I agree that the convexity makes the Schmitt-Conway-Danzer biprism a superior monotile. However, as Warren Smith noted, my Lego aperiodic structure is somewhat different from the SCD tile, in that the union of any finite number of layers is periodic. Also, the tiles interlock (obviously impossible for convex tiles), and thus it's more obvious how to assemble these than SCD biprisms.

George also wrote:

P.S. My latest Simons Foundation video is about math and music:   https://www.simonsfoundation.org/multimedia/mathematical-impressions-making-...

Interesting. I presume this is a discrete analogue of the fact that the space of lines on an affine plane form a topological Möbius strip? Also, I suspect you can apply projective duality to interchange notes and chords. Sincerely, Adam P. Goucher

On 8/23/2013 4:39 PM, Warren D Smith wrote:

...

Hey George Hart, that AP Goucher "lego" is talking to you! It is saying "print me on your 3D printer!" I can hear it!

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