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The components for building a new class of entangled topological structures.
A polyknot is a structure that combines the topology of knots and links with the geometry of polyhedra — organizing knotted or interlinked forms around the faces, edges, or vertices of a polyhedral framework. A mechanical polyknot adds kinetic behavior: the structure physically moves through a controlled, predictable path between states while maintaining its topological integrity. The motion is not added on — it is built into the geometry of the object.
These components — C-hinges, hinged polygon frames, and hinged pyramid frames — are the building blocks for constructing mechanical polyknots and star polyknots. The C-hinge is an original design developed from jdanders' Archipanels hinged polygon system, reconfigured here as a reciprocal coupling element capable of governing coordinated motion across a larger entangled assembly.
With just these three component types, a wide range of polyknot structures becomes physically realizable. This is an open area. Geometric sculptors, mechanical engineers, topologists, and makers interested in kinetic structures will all find something here worth building on.
Some of these are remixes: Many thanks to jdanders for their work and the polypanels by Devin Motes at Make Anything who made the originals that jdanders remixed.
While these structures may be used as toys or fidgets in the spirit of the Hoberman sphere, they are intended to serve as functional models of viable research grade mechanical structures.
These mechanical polyknots (in the photos) are inspired by mathematical artist Rinus Roelofs: Rinus Roelofs - Index and the lithograph 'Gravity' by MC Escher. Collectively, they represent a novel class of mechanical structures with many unique and emergent properties. For example, single structures exhibit global behavior from local activation. When coupled they have additional emergent behaviors that require lengthy descriptions that are not suitable here.
To make a mechanical tetrahedral polyknot you will need:
8 triangular Archipanels
12 C hinges
To make the mechanical cubic polyknot you will need:
12 square Archipanels
24 C hinges
To make the mechanical dodecahedral polyknot you will need:
24 pentagonal Archipanels
60 C hinges
The mechanical octahedral polyknot and the mechanical icosahedral polyknot are structurally unstable. However, there are a wide variety of structures that are possible with unique and interesting kinematic behavior, including 2D-3D actuated structures based on tessellations, nested polyknots, and polyknot networks.
See 2 in action at:
https://www.youtube.com/watch?v=kQpTj5Hh89M
https://www.youtube.com/shorts/kG2VVz8ND6w
For the complete no cost construction system see: Mechanical Polyknot Construction System by APC5 - Thingiverse
Roelofs Mechanical Tetrahedral Polyknot
components: 12 C hinges,
8 triangular hinges
Roelofs Mechanical Cubic Polyknot
components: 24 C hinges,
12 square hinges
Roelofs Mechanical Dodecahedral Polyknot
components: 60 C hinges,
24 pentagonal hinges
Escher Mechanical Polyknot
components: 60 C hinges,
12 pentagonal hinges.
12 pyramidal pentagonal hinges
Roelofs Mechanical Truncated Icosahedral Polyknot
components: 180 C hinges,
12 pentagonal hinges,
20 hexagonal hinges
Roelofs Mechanical Cubic Polyknot
components: 24 C hinges,
12 square hinges
Roelofs Mechanical Double Cubic Polyknot
components: 40 C hinges,
20 square hinges
Roelofs Mechanical Tetracubic Polyknot
components: 48 C hinges,
32 square hinges
Roelofs Mechanical Pentacubic Polyknot
components: 104 C hinges,
60 square hinges
Roelofs Mechanical Trefoil Polyknot
components: 6 C hinges,
6 double triangular hinges
Roelofs Mechanical Tessellated Polyknot
components: 18 C hinges,
8 triangular hinges, 6 hexagonal hinges
Roelofs Mechanical Tessellated Polyknot
components: 24 C hinges,
14 hexagonal hinges
Roelofs Mechanical Polycubic Polyknot
components: 8 C hinges,
44 square hinges
Roelofs Mechanical Tessellated Polyknot
components: 24 C hinges,
12 square hinges
Roelofs Mechanical Fleahedral Polyknot
components: 12 C hinges,
16 square hinges
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