2020 Joint Mathematics Meetings
Laura Shea
Artists
Statement
My work explores complex polyhedral structures and polygon formations created by stitching together beads and thread. My repertoire includes classic geometric forms, whole and partial frame polyhedra, polyhedral complexes that include two or more inter-connected Platonic and Archimedean frame polyhedra, regular tilings, and tessellations. I connect the component forms at contiguous polygonal faces and edges to create chains, sculptural polyhedra and tilings. The open networks of tilings and frame polyhedra provide a magical space for light to play with crystal and glass beads scattering refracted light and creating intriguing, substantial and insubstantial patterns.
Artworks
This motif of hexagons is based on a popular Islamic screen pattern. Beaded frame dodecahedra form six inter-connected hexagons. After discovering that eight dodecahedra will form a diamond or equilateral rhombus (in the plane), I have been experimenting with creating other polygons using dodecahedra for components. I found that I could construct squares, rectangles, hexagons, and six-pointed stars using different combinations of dodecahedra. Because of the nature of the angles of the pentagonal faces of the dodecahedron there are slightly different formulas for making each polygon. I have never seen this hexagonal and six-pointed star combination of dodecahedra anywhere before.
Central top: Pendant Necklace (consisting of of a diamond/rhombus shape made of eight dodecahedra connected to a square of twelve dodecahedra). Left top: diamond/rhombus. Right top: square. Left bottom: rectangle. Right bottom: hexagon. The component dodecahedra are equilateral with one bead per edge. After discovering that eight dodecahedra will form a diamond or equilateral rhombus (in the plane), I discovered that I could form equilateral squares, rectangles, hexagons, and six-pointed stars. (My other submission "Dodedahedron Hexagon Suite" is a six-pointed star.) There are slightly different formulas for making each polygon. I have never seen squares, rectangles, or stars made of combinations of dodecahedra anywhere before.