Mathematics Through 3D Printing is being taught for the first time in the math department at George Mason University.

**Wallpaper groups and their symmetries.**Any pattern that can be repeated in a repeatable fashion throughout the entire infinite plane is mathematically classified as having a specific symmetry, or wallpaper group. There are only 17 possible wallpaper groups. The tiles pictured above each represent distinct wallpaper groups. The tiles are designed and printed on a 3D printer by GMU students as part of the course Mathematics Through 3D Printing, Spring 2016.

**Pentagon tilings and Penrose tilings.**There are only 15 known pentagons which can be used as a single tile in a repeatable periodic fashion throughout the entire infinite plane. In the above display, you can see four of these 15 pentagon tilings. The display also contains two examples of Penrose tilings, which tile the plane

*quasiperiodically*. That is, though they can be used to tile the infinite plane, there is no exact repeat of the pattern (though small portions of the pattern repeat infinitely often). The tiles are designed and printed on a 3D printer by GMU students as part of the course Mathematics Through 3D Printing, Spring 2016.

Now hanging in the GMU Mathematics Tutoring Center:

Here is a list of links of Thingiverse entries, blog posts, and exhibits of materials created by class members. Many contain a description of the object, along with the pattern needed to reproduce the object on your own 3D printer:

Exhibits:

Duality of Platonic and Archimedean Solids

Chaotic Attractors

Surfaces from the Gallery of Famous Surfaces

Thingiverse Entries:

Morphism from the Associahedron to its dual, the Triaugmented Triangular Prism

Rossler Attractor

Julia Set Plot for c = 1/Pi

Mobius strip with Cuboctahedron feet

Rossler Attractor

Julia Set Plot for c = 1/Pi

Mobius strip with Cuboctahedron feet

Snail Shell Curve w/ Parametrization of Curves

Thomas Cyclically Symmetric Attractor

Recursive Triangle

Koch Snowflake-An Iterated Function System

IFS - Iterated Function System

Double Integral Approximation

Thomas Cyclically Symmetric Attractor

Recursive Triangle

Koch Snowflake-An Iterated Function System

IFS - Iterated Function System

Double Integral Approximation

Taylor's Theorem

Riemann Surface of R^1/3

Blog Posts:

Pentagon Tiling 3

Pentagon Tiling

The Rhombicosidodecahedron: More than just a fancy name

Morphing the Snub Dodecahedron

Julia Set

Mandelbrot Set

Rossler Attractor

Lorenz Attractor

Sierpinski Triangle in 3 Dimensions

Fun with Fractals

A game of chaos

Level sets

The T-Square Fractal

The “Not-so-Center” of Mass

Riemann Surface of R^1/3

Blog Posts:

Pentagon Tiling 3

Pentagon Tiling

The Rhombicosidodecahedron: More than just a fancy name

Morphing the Snub Dodecahedron

Julia Set

Mandelbrot Set

Rossler Attractor

Lorenz Attractor

Sierpinski Triangle in 3 Dimensions

Fun with Fractals

A game of chaos

Level sets

The T-Square Fractal

The “Not-so-Center” of Mass

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