Polyknots and Polylinks

Roelofs Polyknots and Polylinks 1

[Polyknot and Polylink Introduction] > [Roelofs Polyknots and Polylinks 1]

Roelofs polyknots and polylinks are derived from convex polyhedra whereas Escher polyknots and polylinks are derived from pyramidally augmented star polyhedra (Figure 1)

base polyhedron

(cube)

derived polyknot

(Roelofs cubic polyknot)

base polyhedron

(star cube)

derived polyknot

(Escher cubic polyknot)

(Figure 1)

Use the guide below to access standardized examples of each subcategory of Roelofs polyknots and polylinks. For additional nonstandard Roelofs Polyknots and Polylinks use this link.

A 360-degree rotating animation of a Roelofs decagonal antiprism polyknot with a crossing number of 60.

Roelofs Antiprism Polylinks

A 360-degree rotating animation of a Roelofs truncated icosidodecahedral polyknot with a crossing number of 360.

Roelofs-Archimedean Polyknots and Polylinks

A 360-degree rotating animation of a Roelofs disdyakistriacontahedral polyknot with a crossing number of 360.

Roelofs-Catalan

Polyknots and Polylinks

A 360-degree rotating animation of a Roelofs pentagonal rotunda polyknot with a crossing number of 70.

Roelofs-Johnson Polyknots and Polylinks

A 360-degree rotating animation of a Roelofs icosahedral polyknot with a crossing number of 60.

Roelofs-Platonic Polyknots and Polylink

A 360-degree rotating animation of a Roelofs decagonal prism polyknot with a crossing number of 60.

Roelofs Prism Polyknots

This collection of 20 nonstandard Roelofs polylinks and polyknots offers a sense of the range of possibilities that their construction with polygons and polyhedra affords.

A 360-degree rotating animation of a Roelofs decagonal cubic polyknot with a crossing number of 24.

structure: Roelofs cubic polyknot

components: cubes

A 360-degree rotating animation of a Roelofs icosahedral polyknot with a crossing number of 60.

structure: Roelofs icosahedral polyknot

components: triangualr prisms, cubes

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: pentagonal prisms cubes

A 360-degree rotating animation of a Roelofs tetrahedral polyknot with a crossing number of 12.

structure: Roelofs tetrahedral polyknot

components: triangles, squares, pentagons

A 360-degree rotating animation of a Roelofs tetrahedral polyknot with a crossing number of 12.

structure: Roelofs tetrahedral polyknot

components: squares, hexagons

A 360-degree rotating animation of a Roelofs tetrahedral polyknot with a crossing number of 12.

structure: Roelofs tetrahedral polyknot

components: squares, hexagons

A 360-degree rotating animation of a Roelofs octahedral polylink with a crossing number of 24.

structure: Roelofs octahedral polylink

components: squares, hexagons

A 360-degree rotating animation of a Roelofs octahedral polylink with a crossing number of 24.

structure: Roelofs octahedral polylink

components: squares, hexagons

A 360-degree rotating animation of a Roelofs octahedral polylink with a crossing number of 24.

structure: Roelofs octahedral polylink

components: squares, hexagons

A 360-degree rotating animation of a Roelofs octahedral polylink with a crossing number of 24.

structure: Roelofs octahedral polylink

components: squares, hexagons

A 360-degree rotating animation of a Roelofs cubic polyknot with a crossing number of 24.

structure: Roelofs cubic polyknot

components: squares, octagons

A 360-degree rotating animation of a Roelofs cubic polyknot with a crossing number of 24.

structure: Roelofs cubic polyknot

components: squares, hexagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: pentagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: squares, pentagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: triangles, pentagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: triangles, pentagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: squares, pentagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: pentagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: pentagons

A 360-degree rotating animation of a Roelofs dodecahedral polyknot with a crossing number of 60.

structure: Roelofs dodecahedral polyknot

components: squares, pentagons

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