Figure Eight Knot Sculpture

Mount Holyoke College is honored to have this special sculpture. It is located on the mid level of the Libary tower (Level 4 stair landing), visible from many directions including from the Reference Room across the court. It was installed in February 1992 in connection with the dedication of the new Science Library.

Eight Knot Sculpture

Hyperbolic Space H3/G

K\PSL2(C)/G

| Z[w]) : G| = 12, w3 = 1

Helaman Ferguson (American, b. 1940)

Carrara Marble, 34" x 24" x 24", 1990

Clues

This sculpture features a sinuous closed curve, a figure-eight knot. The space curve never crosses itself, yet divides the double torus bearing it into two distinct surfaces, one smooth and one textured. This sculpture celebrates among other things the mathematical knowledge that the complement of the figure-eight knot is the quotient of hyperbolic three-space H3 by a discrete arithmetic group. (The figure-eight knot is the only possible arithmetic knot.) The knot complement is homeomorphic to the hyperbolic manifold H3/G where G is a discrete subgroup of index twelve in the Bianchi group PSL2(Z[w]) over the Eisenstein integers Z[w], where w is a cube root of unity. The cube roots of unity form an equilateral triangle which tessellate the plane with hexagons. The honeycomb texture in one of the surfaces was the result of a natural sphere carving process which produces many hexagonal crest arrangements. The knot complement has hyperbolic volume.

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