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(2 3 7) Triangles and Klein's Quartic

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(2 3 7) Triangles and Klein's Quartic

My new favorite t-shirt arrived in the mail today, designed by Henry Segerman.

This design and many others with mathematical themes are available at Henry's website.
http://www.segerman.org/tshirts.html

I used the "create" version of the shop to slightly alter the size and color.
http://math-art-create.spreadshirt.com/us/US/Shop/

So what is this design?

In short, it is a tiling of (2 3 7) triangles.  The (2 3 7) designates a Schwarz triangle.  It means the 3 angles of each triangle are π/2, π/3, and π/7.  Schwarz triangles can tile the sphere, Euclidean plane, or hyperbolic plane depending on the choice of the 3 angles.  (2 3 7) triangles tile the hyperbolic plane, and Henry has drawn these triangles in the Poincare disk model, cutting off the model at some radius from the origin. 

My G+ banner is a similar representation of (2 3 7) triangles tiling the disk, but with a different choice of cutoff and as a 3D printed model.  I previously …

I recommend watching the talks too!

I recommend watching the talks too!

Originally shared by Henry Segerman

This is a walkthrough of Saul Schleimer's and my art exhibition at the Simons Center for Geometry and Physics at Stony Brook. 

The posters are available at https://www.dropbox.com/sh/ycugkbxmii1k9zf/AACdkp0C5LV8FvBBw0-GiMAga
The catalog is available at http://www.math.okstate.edu/~segerman/exhibitions/illustrating_geometry_catalog.pdf
We gave two talks, which can be viewed at "Illustrating Geometry" exhibition at SCGP, Artist's talk: "Sculpture in four-dimensions" and "Illustrating Geometry" exhibition: Artist's talk by Saul Schleimer: "Minimal and Seifert Surfaces"

Many thanks to Maria Froehlich, Tim Young, Katherine Schwarting and Margaret Schedel for all of their help, and to George Hart for helping us with dyeing some of the sculptures. Thanks also to the Museum of Mathematics and Tony Phillips for the loan of their artworks for the show.
http://www.youtube.com/watc…