Polyknots and Polylinks

Roelofs-Catalan Polyknots and Polylinks RC1-RC13

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

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

base polyhedron

(pentakisdodecahedron)

derived polyknot

(Roelofs pentakisdodecahedral polyknot)

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 a Roelofs triakistetrahedron polyknot with a crossing number of 36.

structure: Roelofs triakistetrahedron polyknot

RC1

components: triangles

A 360-degree rotating animation of a Roelofs rhombic dodecahedron polyknot with a crossing number of 48.

structure: Roelofs rhombic dodecahedron polyknot

RC2

components: triangles

A 360-degree rotating animation of a Roelofs tetrakishexahedron polyknot with a crossing number of 72.

structure: Roelofs tetrakishexahedron polyknot

RC3

components: triangles

A 360-degree rotating animation of a Roelofs triakisoctahedron polyknot with a crossing number of 72.

structure: Roelofs triakisoctahedron polyknot

RC4

components: triangles

A 360-degree rotating animation of a Roelofs strombic icositetrahedron polyknot with a crossing number of 96.

structure: Roelofs strombic icositetrahedron polyknot

RC5

components: triangles

A 360-degree rotating animation of a Roelofs disdyakisdodecahedron polyknot with a crossing number of 144.

structure: Roelofs disdyakis-dodecahedron polyknot

RC6

components: triangles

A 360-degree rotating animation of a Roelofs pentagonal icitetrahedron polyknot with a crossing number of 120.

structure: Roelofs pentagonal icositetrahedron polyknot

RC7

components: triangles

A 360-degree rotating animation of a Roelofs rhombic triacontahedron polyknot with a crossing number of 120.

structure: Roelofs rhombic triacontahedron polyknot

RC8

components: triangles

A 360-degree rotating animation of a Roelofs pentakisdodecahedron polyknot with a crossing number of 180.

structure: Roelofs pentakisdodecahedron polyknot

RC9

components: triangles

A 360-degree rotating animation of a Roelofs triakisicosahedron polyknot with a crossing number of 180.

structure: Roelofs triakisicosahedron polyknot

RC10

components: triangles

A 360-degree rotating animation of a Roelofs strombic hexecontahedron polyknot with a crossing number of 240.

structure: Roelofs strombic hexecontahedron polyknot

RC11

components: triangles

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

structure: Roelofs disdyakistria-contahedron polyknot

RC12

components: triangles

A 360-degree rotating animation of a Roelofs pentagonal hexacontahedron polyknot with a crossing number of 300.

structure: Roelofs pentagonal hexacontahedron polyknot

RC13

components: triangles

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