# Mathematical Imagery

Mathematical artists create strong, stunning works in all media and explore the visualization of mathematics

# Woven Beads :: Gwen L. Fisher

[Above Unlikely Tetrahedron views] Materials: size 15° seed beads, 3 mm bugle beads, 3 mm Swarovski crystal, thread. 34 mm on an edge. I applied the beading techniques I used to turn Impossible Triangles into beaded art objects to a tetrahedron. The Unlikely Tetrahedron generates no corresponding optical illusion. The faces form three distinct paths that twist around the sculpture in unexpected ways. Each beam includes all three colors of faces, with one color on two opposite faces. Like a Möbius band, as you follow a path around the piece, sometimes when you get back to a beam, you return to the opposite face. Thus, it feels like you have to travel around the sculpture twice just to get back to where you started.

[Above Unlikely Dodecahedron views] Materials: size 15° and 11° seed beads and thread. 23 mm on an edge, 58 mm diameter. I applied the beading techniques I used to turn Impossible Triangles into beaded art objects to a dodecahedron. The Unlikely Dodecahedron generates no corresponding optical illusion. The faces form ten distinct paths that twist around the sculpture in unexpected ways.

Materials: size 11° seed beads and thread. 63 mm diameter. This is a beaded version of the hyperbolic rhombitetrahexagonal tiling. This tiling is composed of squares and hexagons with three squares and one hexagon around every vertex. I made two of the types of squares green to emphasize the stripes in the tiling. The other type of square is purple, and the hexagons are pink. To make this tiling with bead weaving, I used an across-edge weave. In particular, for the squares, I weaved loops of four beads of the same color for each square, and loops of 6 beads for the hexagons. Then, I attached the loops with one bead per adjacent pair. So the holes of the beads that lie on the edges of the tiling are perpendicular to the the edges.

Materials: size 11° and 15° seed beads and thread. 34 mm diameter. Beaded knots are quite flexible. You can turn them inside out, and they can be worn as finger rings, of flatten them to make rosettes for pendants or earrings. This knot is a Brunnian link, meaning that if any one component is removed, then the remaining pieces are unlinked unknots.