[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)
structure: Escher triakistetrahedral polyknot
EC1
components: triangles
structure: Escher rhombic dodecahedral polyknot
EC2
components: triangles
structure: Escher tetrakishexahedral polylink
EC3
components: triangles
structure: Escher triakisoctahedral polyknot
EC4
components: triangles
structure: Escher strombic icositetrahedral polyknot
EC5
components: triangles
structure: Escher disdykakis-dodecahedral polylink
EC6
components: triangles
structure: Escher pentagonal icositetrahedral polyknot
EC7
components: triangles
structure: Escher rhombic triacontahedral polyknot
EC8
components: triangles
structure: Escher pentakisdodecahedral polyknot
EC9
components: triangles
structure: Escher triakisicosahedral polyknot
EC10
components: triangles
structure: Escher strombic hexecontahedral polyknot
EC11
components: triangles
structure: Escher disdykakistria-contahedral polylink
EC12
components: triangles
structure: Escher pentagonal hexecontahedral polyknot
EC13
components: triangles