Bridges 2024 Exhibition of Mathematical Art, Craft, and Design

# Gabriel Frampton

## Artists

## Statement

My origami work is an attempt to give ideal mathematical forms physical representation. Through years of experimentation, I developed a new method of weaving strips together to create geometrical shapes. This approach has the advantage of offering physical strength to the finished designs, which in effect become tensegrity sculptures. My designs draw from the topology of knots, translating a set of interlocking loops into flat strips of varying lengths. Originally I worked in paper, but have moved to more durable materials as the complexity of the designs increased. My current works use Dura-Lar film, which is large and strong enough to make polyhedra a meter in diameter.

## Artworks

This surface can be visualised as primarily composed of ninety hexagons - 15 pairs of parallel hexagons radiate out from the origin. The remaining 60 are less obvious - by folding each hexagon in half, groups of five form 12 star-shaped tubes. To complete the surface, 90 triangular facets form the tetrahedral cups and pentagonal faces. It is an example of a nolid, with no enclosed volume. This modular origami piece is a knotted polylink of 80 closed loops, which follow the symmetry of an icosahedron: 30 edges, 20 triangular faces, 24 pentagonal vertices (12 left-handed & 12 right-handed), and 6 equatorial bands. These loops are further divided into overlapping segments, which brings the total number of pieces to 300.