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The 5 Escher-Platonic Polyknots

This collection includes one Escher octahedral polylink and the other four are polyknots. They have knots at each vertex of the base polyhedron from which they are derived corresponding to its vertex configuration. For example, the…

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The 5 Roelofs-Platonic Polyknots

This collection includes one Roelofs octahedral polylink and the other four are polyknots. They have knots at each vertex of the base polyhedron from which they are derived corresponding to its vertex configuration. For example, the…

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7 Roelofs Prism Polyknots

These are 3D knots with prism symmetries: triangular to decagonal prisms (less the cubic polyknot) are represented. Recommended with tree supports and a z-axis setting of at least 60mm.

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5 Escher Antiprism Polyknots

These are 3D knots with antiprism symmetries. tree supports are recommended and a minimum of 70mm z-axis setting

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7 Roelofs Antiprism Polyknots

these are 3D knots with antiprism symmetries. it is recommended that the z-axis setting be 50mm or greater and that tree supports be used.

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ESCHER NESTED STAR DODECAHEDRAL POLYKNOT 2

a nested polyknot inspired by MC Escher Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 14

a polyknot inspired by MC Escher Category: Math Art

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ROELOFS RHOMBIC DODECAHEDRAL POLYKNOT 2

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS TETRAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS CUBIC POLYKNOT 5

a polyknot inspired by Rinus Roelofs Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 13

a polyknot inspired by MC Escher Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 12

a polyknot inspired by MC Escher Category: Math Art

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ROELOFS PENTAGONAL PRISMIC POLYKNOT 1

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS CUBIC POLYKNOT 6

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS CUBIC POLYKNOT 5

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS CUBIC POLYKNOT 4

a polyknot inspired by Rinus Roelofs Category: Math Art

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ESCHER STAR OCTAHEDRAL POLYKNOT 1

a polyknot inspired by MC Escher Category: Math Art

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STEWART DODECAHEDRAL POLYKNOT 1

a polyknot inspired by BM Stewart Category: Math Art

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ROELOFS DODECAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs Category: Math

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KEPLER STAR DODECAHEDRAL POLYKNOT 1

a polyknot inspired by Johannes Kepler Category: Math Art

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ESCHER Z STAR DODECAHEDRAL POLYKNOT 1

a polyknot inspired by MC Escher Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 8

a polyknot inspired by MC Escher Category: Math Art

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ROELOFS TETRAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS DODECAHEDRAL POLYKNOT 1

a polyknot inspired by MC Escher, Rinus Roelofs, and Alan Holden Category: Math Art

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ROELOFS-ESCHER TETRAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs and MC Escher Category: Math Art

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ROELOFS RHOMBIC DODECAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS OCTAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs Category: Math Art

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KEPLER-ROELOFS CUBIC POLYKNOT 1

a polyknot inspired by Rinus Roelofs and Johannes Kepler Category: Math Art

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ROELOFS CUBIC POLYKNOT 2

a polyknot inspired by Rinus Roelofs Category: Math Art

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KEPLER-ROELOFS OCTAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs and Johannes Kepler Category: Math Art

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ROELOFS OCTAHEDRAL POLYKNOT 1

a polyknot inspired by Rinus Roelofs Category: Math Art

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NESTED ESCHER STAR DODECAHEDRAL POLYKNOT 1

a polyknot inspired by MC Escher Category: Math

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ESCHER STAR DODECAHEDRAL POLYKNOT 7

a polyknot inspired by MC Escher Category: Math

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ESCHER STAR DODECAHEDRAL POLYKNOT 6

a polyknot inspired by MC Escher Category: Math

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ESCHER STAR DODECAHEDRAL POLYKNOT 5

a polyknot inspired by MC Escher Category: Math

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ESCHER STAR DODECAHEDRAL POLYKNOT 3

a polyknot inspired by MC Escher Category: Math

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ESCHER STAR DODECAHEDRAL POLYKNOT 2

a polyknot inspired by MC Escher Category: Math

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ESCHER STAR DODECAHEDRAL POLYKNOT 1

a polyknot inspired by MC Escher Category: Math

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Mechanical Polyknot Construction with C-Hinges

C-Hinge Assembly for Polyknot Construction The components for building a new class of entangled geometric structures. A polyknot is a structure that combines the topology of knots and links with the geometry of polyhedra — organizing…

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Buildable Escher-Platonic Polyknots (and Polylink) with Archipanels

With these four components you can make three different Escher polyknots and a polylink. The Escher dodecahedral polyknot component will come later. The triangle Archipanel and square Archipanel by jdanders are included for convenience…

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Roelofs Triple Layer Cubic Polyknot 1

This is a 3 layer cubic polyknot inspired by mathematical artist Rinus Roelofs.

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The 5 Escher-Platonic Polyknots

This collection includes one Escher octahedral polylink and the other four are polyknots. They have knots at each vertex of the base polyhedron from which they are derived corresponding to its vertex configuration. For example, the…

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The 5 Roelofs-Platonic Polyknots

This collection includes one Roelofs octahedral polylink and the other four are polyknots. They have knots at each vertex of the base polyhedron from which they are derived corresponding to its vertex configuration. For example, the…

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7 Roelofs Prism Polyknots

These are 3D knots with prism symmetries: triangular to decagonal prisms (less the cubic polyknot) are represented. Recommended with tree supports and a z-axis setting of at least 60mm.

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5 Escher Prism Polyknots

these are 3D polyknots modeled on the prisms and inspired by MC Escher. recommended tree supports and z-axis setting of at least 60mm.

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5 Escher Antiprism Polyknots

These are 3D knots with antiprism symmetries. tree supports are recommended and a minimum of 70mm z-axis setting

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7 Roelofs Antiprism Polyknots

these are 3D knots with antiprism symmetries. it is recommended that the z-axis setting be 50mm or greater and that tree supports be used.

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13 Escher-Catalan Polyknots (complete set)

I have not printed these, but I imagine them to be torture tests for any 3D printer. Based on other polyknots I've printed, I would suggest a z-axis setting of no less than 125mm and tree supports.

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13 Escher-Archimedean Polyknots (complete set)

These are complex models and will be a torture test for any 3D printer. I have not printed them. Based on other polyknots I've printed, I would recommend a z-axis setting of no less than 125mm and tree supports.

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13 Roelofs-Catalan Polyknots (complete set)

This collection of the Roelofs-Catalan polyknots will challenge any 3D printer. Recommendations: z-axis setting 125+mm Tree supports.

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13 Roelofs-Archimedean Polyknots (complete set)

These polyknots will challenge any 3D printer. recommendations: z-axis setting 125+mm tree supports.

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All 92 Roelofs-Johnson Polyknots (complete set)

These polyknots like all polyknots are knots with polyhedral symmetries or in this case asymmetries. To calculate the crossing numbers for these 3D knots, multiply the number of vertices of the base polyhedron by its vertex configuration.…

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ESCHER DODECAHEDRAL POLYKNOT 45

This is a strutted dodecahedral polyknot inspired by MC Escher. Caution: it has sharp points. Not suitable for children. recommended settings: minimum of 150mm z-axis setting tree supports I've printed this. It came out clean and crisp.…

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1 STEWART POLYKNOT & 1 STEWART POLYLINK

a polyknot and a polylink inspired by BM Stewart Category: Math Art

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STEWART POLYKNOT "JITTER KNOT" 2

a jitter knot inspired by BM Stewart Category: Math Art

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DA VINCI ICOSAHEDRAL POLYKNOT 1

an elevated polyknot inspired by the elevated polyhedra of Leonardo da Vinci Category: Math Art

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DA VINCI ELEVATED DODECAHEDRAL POLYKNOT 1

a dodecahedral polyknot inspired by the elevated polyhedra of Leonardo da Vinci Category: Math Art

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HART DODECAHEDRAL POLYKNOT 2

a polyknot inspired by sculptor George Hart More of my math art can be seen at: https://sites.google.com/view/structuralgeometry/home Category: Math Art

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The 13 ROELOFS-CATALAN POLYKNOTS (complete set)

all 13 of the Roelofs-Catalan polyknots: Key to the Roelofs-Catalan poyknots: C1: triakistetrahedron C2: rhombic dodecahedron C3: tetrakishexahedron C4: triakisoctahedron C5: strombic icositetrahedron C6: disdyakisdodecahedron C7:…

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5 ROELOFS-PRISM POLYKNOTS

5 of the infinite Roelofs-Prism polyknots key to the polyknots PR3: triangular prism PR5: pentagonal prism PR6: hexagonal prism PR7: heptagonal prism PR8: octagonal prism Category: Math Art

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The 5 ROELOFS-PLATONIC POLYKNOTS (complete set)

all 5 of the Roelofs-Platonic polyknots inspired by Rinus Roelofs and modeled on the Platonic Solids Key to the polyknots P1: tetrahedron P2: cube P3: octahedron (polylink) P4: dodecahedron P5: icosahedron Category: Math Art

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5 ESCHER-ANTIPRISM POLYKNOTS

5 of the infinite antiprismic polyknots key to the polyknots AP 1: square antiprism AP2: pentagonal antiprism AP3: hexagonal antiprism AP4: heptagonal antiprism AP5: octagonal antiprism Category: Math Art

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5 ESCHER-PRISM POLYKNOTS

5 of the infinite prismic polyknots Key to the polyknots triangualr prism pentagonal prism hexagonal prism Heptagonal prism octagonal prism Category: Math Art

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THE 5 ESCHER-PLATONIC POLYKNOTS (complete set)

all 5 of the Escher-Platonic polyknots Key to the polyknots P1: tetrahedron P2 octahedron P3: cube P4: dodecahedron P5: icosahedron Category: Math Art

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All 13 of the ESCHER-CATALAN POLYKNOTS (Complete Set)

All 13 of the Escher-Catalan polyknots: complete set Key to the polyknots: C1: triakistetrahedron C2: rhombic dodecahedron C3: tetrakishexahedron C4: triakisoctahedron C5: strombic icositetrahedron C6: disdyakisdodecahedron C7: pentagonal…

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All 13 of the ESCHER-ARCHIMEDEAN POLYKNOTS A1-A13 (Complete set)

All 13 of the ESCHER-ARCHIMEDEAN POLYKNOTS A1-A13 (Complete set) Key to the polyknots A1: truncated tetrahedron A2: cuboctahedron A3: truncated octahedron A4: truncated cube A5: rhombicuboctahedron A6: truncated cuboctahedron A7: snub…

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All 13 of the ROELOFS-ARCHIMEDEAN POLYKNOTS: A1-A13 (complete set)

all 13 of the Roelofs-Archimedean polyknots A1-A13. Key to the polyknots A1: truncated tetrahedron A2: cuboctahedron A3: truncated octahedron A4: truncated cube A5: rhombicuboctahedron A6: truncated cuboctahedron A7: snub cube A8:…

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All 92 of the 92 ROELOFS-JOHNSON POLYKNOTS: J1-J92

All 92 of the 92 Roelofs-Johnson polyknots inspired by Rinus Roelofs and modeled on the Johnson solids. (Complete set) Key to the Roelofs-Johnson polyknots: J1: square pyramid J2: pentagonal pyramid J3: triangular cupola J4: square cupola…

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All 92 ESCHER-JOHNSON POLYKNOTS J1-J92 (Complete Set)

All 92 Escher-Johnson polyknots inspired by MC Escher and modeled on the Johnson solids. Complete set Key to the Escher-Johnson polyknots: J1: square pyramid J2: pentagonal pyramid J3: triangular cupola J4: square cupola J5: pentagonal…

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ROELOFS ICOSAHEDRAL POLYKNOT 2

an icosahedral polyknot inspired by Rinus roelofs Category: Math Art

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ESCHER DODECAHEDRAL POLYKNOT 26

A polyknot inspired by MC Escher. I recommend at least a 150 mm z-axis setting to allow for post print support removal. I used tree supports with good result. Category: Math Art

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ESCHER-STEWART STAR DODECAHEDRAL POLYKNOT 1

a star polyknot inspired by MC Escher and BM Stewart Category: Math Art

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GROSSMAN TRUNCATED ICOSAHEDRAL POLYKNOT 1

a polyknot inspired by Bathsheba Grossman Category: Math Art

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ROELOFS STAR OCTAHEDRAL POLYKNOT 1

a star polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS STAR TETRAHEDRAL POLYKNOT 1

a star polyknot with tetrahedral symmetry inspired by artist Rinus Roelofs Category: Math Art

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ROELOFS STAR ICOSAHEDRAL POLYKNOT 1

a star polyknot inspired by mathematical artist Rinus Roelofs Category: Math Art

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ROELOFS TETRAHEDRAL POLYKNOT 2

a remastered Roelofs tetrahedral polyknot inspired by internationally renowned mathematical artists Rinus Roelofs Category: Math Art

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ROELOFS CUBIC STAR POLYKNOT 1

a star polyknot inspired by Rinus Roelofs recommendations: z-axis setting: 125mm+ tree supports comments: simple post print processing Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 5

a star polyknot inspired by MC Escher Category: Math Art

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HART STAR DODECAHEDRAL POLYKNOT 3

a polyknot inspired by George Hart Category: Math Art

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HART STAR DODECAHEDRAL POLYKNOT 2

a polyknot inspired by George Hart Category: Math Art

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ESCHER OCTAHEDRAL POLYKNOT 3

a polyknot with octahedral symmetry Category: Math Art

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ROELOFS DODECAHEDRAL POLYKNOT 4

a polyknot inspired by Rinus Roelofs Category: Math Art

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ROELOFS STAR DODECAHEDRAL POLYKNOT 3

a star polyknot inspired by Rinus Roelofs Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 4

a start dodecahedral polyknot Category: Math Art

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ROELOFS STAR DODECAHEDRAL POLYKNOT 2

a star polyknot inspired by mathematical artist Rinus Roelofs Category: Math Art

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ROELOFS STAR DODECAHEDRAL POLYKNOT 1

a star polyknot inspired by mathematical artist Rinus Roelofs Category: Math Art

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STEWART ICOSIDODECAHEDRAL POLYKNOT 1

a polyknot inspired by BM Stewart with icosidodecahedral symmetry Category: Math Art

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ROELOFS STAR DODECAHEDRAL POLYKNOT 6

a polyknot inspired by Rinus Roelofs Category: Math Art

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GROSSMAN ICOSAHEDRAL POLYKNOT 1

a polyknot inspired by Bathsheba Grossman Category: Math Art

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WEBB ICOSAHEDRAL POLYKNOT 1

a polyknot inspired by Robert Webb Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 18

a polyknot inspired by MC Escher Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 19

a polyknot inspired by MC Escher Category: Math Art

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Escher star dodecahedral polyknot 5

a polyknot inspired by MC Escher Category: Math Art

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ROELOFS DODECAHEDRAL POLYKNOT 3

a polyknot inspired by Rinus Roelofs Category: Math Art

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9 ESCHER PRISMIC POLYKNOTS

a collection of 9 Escher polyknots based on the triangular, pentagonal, hexagonal, heptagonal, octagonal, nonagonal, decagonal, hendecagonal, and the dodecagonal prisms inspired by MC Escher Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 15

a polyknot inspired by MC Escher Category: Math Art

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ESCHER STAR TETRAHEDRAL POLYKNOT 3

a polyknot inspired by MC Esscher Category: Math Art

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HART TRUNCATED STAR DODECAHEDRAL POLYKNOT 2

a polyknot inspired by George Hart Category: Math Art

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ESCHER STAR DODECAHEDRAL POLYKNOT 17

a polyknot inspired by MC Escher Category: Math Art