Topological Nets that Overlap

Knots

[Making Math Models] > [Topological Nets] > [Knots]

The knots below are inspired by knot theory in topology. To make them, an odd number of strips of polygons are assembled and then folded so that they over and underlap as seen below for a trefoil knot. The remainder are left as inspiration and puzzles to be solved.

1 of 3 trefoil knot substructures

assembled substructures

folded assembly

completed trefoil knot

1 of 3 trefoil knot substructures

assembled substructures

folded assembly

completed trefoil knot

An assembled topological net for an 8-crossing knot built with squares.

structure: 8 crossing knot

components: squares

An assembled topological net for trefoil knot built with squares and hexagons.

structure: Kepler trefoil knot

components: squares, hexagons

An assembled topological net for a cylinder trefoil knot built with squares.

structure: cyclinder trefoil knot

components: squares

An assembled topological net for a pentagram pentafoil knot built with squares.

structure: cyclinder pentagram knot

components: squares

An assembled topological net for a Kepler trefoil knot built with triangles and squares.

structure: Kepler trefoil knot

components: triangles, squares

An assembled topological net for a pentagram pentafoil knot built with squares and pentagons.

structure: Kepler pentagram knot

components: squares, pentagons

An assembled topological net for a forever knot built with squares.

structure: forever knot

components: squares

An assembled topological net for a 10-crossing knot built with squares and pentagons.

structure: 10 crossing knot

components: squares, pentagons

An assembled topological net for a pentafoil knot built with squares and decagons.

structure: pentafoil knot

components: squares, decagons

An assembled topological net for a pentafoil knot built with squares and pentagons.

structure: pentafoil knot

components: squares, pentagons

An assembled topological net for a pentafoil knot built with squares and decagons.

structure: pentafoil knot

components: squares, decagons

An assembled topological net for a pentafoil knot built with squares and decagons.

structure: pentafoil knot

components: squares, decagons

An assembled topological net for a pentafoil knot built with squares and pentagons.

structure: pentafoil knot

components: squares, pentagons

An assembled topological net for a heptafoil knot built with squares and heptagons.

structure: heptafoil knot

components: squares, heptagons

An assembled topological net for a heptafoil knot built with squares and heptagons.

structure: heptafoil knot

components: squares, heptagons

An assembled topological net for a nonafoil knot built with squares and nonagons.

structure: nonafoil knot

components: squares, nonagons

An assembled topological net for a decafoil knot built with squares, pentagons, and decagons.

structure: decafoil knot

components: squares, pentagons, decagons

An assembled topological net for a 14-crossing knot built with squares and heptagons.

structure: 14 crossing knot

components: squares, heptagons

An assembled topological net for a16-crossing knot built with squares and octagons.

structure: 16 crossing knot

components: squares, octagons

An assembled topological net for a icosafoil knot built with squares, pentagons, and decagons.

structure: icosafoil knot

components: squares, pentagons, decagons

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