2022 Joint Mathematics Meetings

# Nathan Fieldsteel, Jessica Appel, Katie Davenport, Sean Grate, Madison Howard, Dave Jensen, Jenny Kenkel, Chris Manon, Owen McGrath, Jackson Morris, Laura Reese, Kate Ponto, Kathryn Schantz, and Angela Vichitbandha

## Artists

## Statement

The University of Kentucky Math Lab aims to encourage undergraduate math interest across a range of projects. These include research projects and outreach as well as visualization projects. We interpret visualization broadly making room for both 3d printing of polyhedra, simplicial complexes, and string diagrams and more traditional textile crafts such as quilting and crochet.

## Artworks

This is a Cayley table for the symmetric group on four letters. Each element has a color and the colors are arranged to show subgroups and quotients. The 12 by 12 block consisting of the warm colored squares is the alternating group on four letters. The Klein four group is the 4 by 4 block of yellow squares. Both of these subgroups are normal. The top 2 by 2 square is cyclic of order 2 and not normal.
To see quotients allow similar colors to blur together. For the quotient by the alternating group blur the warm colored squares together and the cool colored squares together. For the quotient by the Klein four group merge the yellow squares together and the same for orange, red, blue, green, and purple.