##### Department of Mathematics,

University of California San Diego

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### Math 196 - Student Colloquium

## Justin Roberts

#### UCSD

## Mathematical Crystallography

##### Abstract:

A crystal is a shape which tessellates the plane (or space) in a periodic way, so that the pattern repeats at regular intervals in all directions. The group of symmetries (translational, rotational, reflectional) of such a tessellation is called a crystallographic group. In two dimensions there are exactly 17 different kinds of symmetry, the so-called "wallpaper groups", which I'll describe. I'll also mention what happens in three dimensions, in hyperbolic space, and how you can make "quasiperiodic" tessellations (Penrose tilings) with five-fold symmetry.

### October 21, 2014

### 12:00 PM

### AP&M B402A

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