Polyknots and Polylinks

Escher-Catalan Polyknots and Polylinks EC1-EC13

[Polyknot and Polylink Introduction] > [Escher Polyknots and Polylinks] > [Escher-Catalan Polyknots and Polylinks]

The base polyhedra for these polyknots and polylinks are the Catalan polyhedra as for example the pentakisdodecahedron and the Escher pentakisdodecahedral polyknot (Figure 1).

base polyhedron

(pentakisdodecahedron)

derived polyknot

(Escher pentakisdodecahedral polyknot)

(Figure 1)

It remains an open question which of the Catalans are polyknots or polylinks as they have two or more different vertex configurations. The remaining data is presented below (Table 1).

(Table 1)

A 360-degree rotating animation of an Escher triakistetrahedral polyknot with a crossing number of 36.

structure: Escher triakistetrahedral polyknot

EC1

components: triangles

A 360-degree rotating animation of an Escher rhombic dodecahedral polylink with a crossing number of 36.

structure: Escher rhombic dodecahedral polyknot

EC2

components: triangles

A 360-degree rotating animation of an Escher tetrakishexahedral polyknot with a crossing number of 72.

structure: Escher tetrakishexahedral polylink

EC3

components: triangles

A 360-degree rotating animation of an Escher triakisoctahedralpolyknot with a crossing number of 72.

structure: Escher triakisoctahedral polyknot

EC4

components: triangles

A 360-degree rotating animation of an Escher strombic icositetrahedral polyknot with a crossing number of 96.

structure: Escher strombic icositetrahedral polyknot

EC5

components: triangles

A 360-degree rotating animation of an Escher disdykakisdodecahedral polylink with a crossing number of 120.

structure: Escher disdykakis-dodecahedral polylink

EC6

components: triangles

A 360-degree rotating animation of an Escher pentagonal icositetrahedral polyknot with a crossing number of 120.

structure: Escher pentagonal icositetrahedral polyknot

EC7

components: triangles

A 360-degree rotating animation of an Escher rhombic triacontahedral polyknot with a crossing number of 120.

structure: Escher rhombic triacontahedral polyknot

EC8

components: triangles

A 360-degree rotating animation of an Escher pentakisdodecahedral polyknot with a crossing number of 180.

structure: Escher pentakisdodecahedral polyknot

EC9

components: triangles

A 360-degree rotating animation of an Escher triakisicosahedral polyknot with a crossing number of 180.

structure: Escher triakisicosahedral polyknot

EC10

components: triangles

A 360-degree rotating animation of an Escher strombic hexecontahedral polyknot with a crossing number of 240.

structure: Escher strombic hexecontahedral polyknot

EC11

components: triangles

A 360-degree rotating animation of an Escher disdykakiscontahedron polylink with a crossing number of 360.

structure: Escher disdykakistria-contahedral polylink

EC12

components: triangles

A 360-degree rotating animation of an Escher pentagonal hexecontahedral polyknot with a crossing number of 300.

structure: Escher pentagonal hexecontahedral polyknot

EC13

components: triangles

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