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Title: Trefoils
Artist and Designer: Hugh
Griffiths Hugh's knitting blog
Materials: Patons DK yarn
Technique: Knit
Artist’s Statement: The left and right trefoils are the simplest
non-trivial knots. Despite being mirror images, it is impossible to smoothly
deform one knot into the other—a result which can be shown by calculating the
Jones polynomials of the two knots. The surfaces, however, are homeomorphic—both
are homeomorphic to a torus, illustrating the important distinction between
the intrinsic geometry of a surface and its embedding into space.