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Escher polyknots are star knots that terminate with pyramids and exhibit polyhedral symmetries or asymmetries. Inspired by Johannes Kepler’s annuloid studies and M.C. Escher’s 1952 lithograph Gravity, these polyknots appear in chiral pairs, though only one of each pair is typically displayed. Each polyknot forms a knot at the vertices of its base polyhedron, with the type of knot determined by the vertex number, which corresponds to the vertex configuration of the base polyhedron.
The crossing number of a polyknot is calculated by multiplying the number of vertices of the base polyhedron by its vertex number. For example, a cubic polyknot, based on a cube with 8 vertices and a vertex number of 3, results in a crossing number of 8 × 3 = 24.
This section features over 150 Escher polyknots, including those based on the five Escher-Platonic, thirteen Escher-Archimedean, thirteen Escher-Catalan, five Escher-Prism, five Escher-Antiprism, and ninety-two Escher-Johnson polyknots.
The polyknots on this page are both Escher and Kepler-Escher polyknot; the latter are informed by the polygon studies of Johannes Kepler.
structure: Escher dodecahedral polyknot
components: pentagons, hexagons
structure: Kepler-Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons, decagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons, decagons
structure: Escher dodecahedral polyknot
components: squares, triangles, decagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons, decagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons, decagons
structure: Escher dodecahedral polyknot
components: hexagons, triangles, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher octahedral polyknot
components: squares, triangles, hexagons
structure: Escher dodecahedral polyknot
components: squares, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher-Kepler dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher icosahedral polyknot
components: triangles, pentagons
structure: Escher dodecahedral polyknot
components: squares, triangles, pentagons
structure: Escher dodecahedral polyknot
components: triangles, pentagons
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