# Conan Chadbourne

My work is motivated by a fascination with the occurrence of mathematical and scientific imagery in traditional art forms, and the frequently mystical or cosmological significance that can be attributed to such imagery. Mathematical themes both subtle and overt appear in a broad range of traditional art, from Medieval illuminated manuscripts to Buddhist mandalas, intricate tilings in Islamic architecture to restrained temple geometry paintings in Japan, complex patterns in African textiles to geometric ornament in archaic Greek ceramics. Often this imagery is deeply connected with how these cultures interpret and relate to the cosmos, in much the same way that modern scientific diagrams express a scientific worldview. I am especially interested in symmetry as a mechanism for finding order in the universe, from its intuitive appearance in ancient cosmological diagrams to its important role in modern theoretical physics, and my recent works explore various forms of symmetry.

This work belongs to a series of images which explore the structure of the alternating group on five elements (A5), also known as the icosahedral group. This image is based on a particular presentation of A5 given by two generators of orders 3 and 5, shown in green and blue, respectively. The elements of the group are associated with the faces of one of the Catalan Solids, the tetragonal hexecontahedron, shown here projected into the plane. The edges of this polyhedron form the dual graph to the Cayley diagram for this presentation of the group, and indicate the relationship between the generators and the group elements. Different textures are applied to the spaces representing the group elements according to their conjugacy classes.

The image is constructed from multiple hand-drawn elements and natural textures which are scanned and digitally manipulated to form a composite image and subsequently output as an archival digital print.

This image uses a presentation of the icosahedral group given by generators of orders 2 and 3, shown in orange and green, respectively. The elements of the group are represented by the sixty triangular faces of the triakis icosahedron, projected into the plane.

This image uses a presentation of the icosahedral group given by three generators of orders 2, 3, and 5, shown in orange, green, and blue, respectively. The elements of the group are represented by the sixty faces of the pentagonal hexecontahedron, projected into the plane.