# Hope Hickman

Artist/ Mathematics Student
University of Akron
Ohio, USA

The following work was pulled from the collection titled "Abstracting Algebra". That which extends the idea of Cayley Diagrams. Pieces are based off small, finite groups, which generate the shape and behavior of their three dimensional counterparts. The work aims to highlight the movement that finite groups posses. By translating 2-D nodes into 3-D columns and 2-D lines into curves in 3-D space, blueprints for the following sculptures are created. The result is organic, intuitive and alive.

Symmetric Group of Order 6
40 x 30 x 30 cm
Stoneware, acrylic paint
2016

The above sculpture is an artistic representation of the finite group S3 (symmetric group of order 6). By supplementing 2-D nodes with 3-D columns and lines in 2-D space with curves in 3-D space, I was able to transform the simplistic Cayley Diagram of S3 into a 3-D sculpture, highlighting movement, symmetry and beauty within the small group. To help understand the construction of the sculpture I have a visual aid that diagrams the blueprints while showing the obvious relationship with S3.

Cyclic Group of Order 6
45 x 30 x 30 cm
Stoneware, acrylic paint
2016

The above sculpture is an artistic representation of the finite group Z6 (cyclic group of order 6). By supplementing 2-D nodes with 3-D columns and lines in 2-D space with curves in 3-D space, I was able to transform the simplistic Cayley Diagram of Z6 into a 3-D sculpture, highlighting movement, symmetry and beauty within the small group. To help understand the construction of the sculpture I have a visual aid that diagrams the blueprints while showing the obvious relationship with Z6. Interestingly, this method of creating a sculpture from a cyclic Cayley Diagram, yields the creation of another larger group, one that plays with the idea of multiple dimensions in a very fun way.