Math 493: Mathematics Through 3D Printing

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:

Planar P3 Penrose Tiling

Dual Solids, Morphing a Truncated Dodecahedron into a Triakis Icosahedron-Project 3

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

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

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