Mechanical Polyknot Construction System

There are 8 remixes of archipanels: 6 pyramids and 2 C hinges that can be used to make mechanical polyknots.
C-Hinge Assembly for Polyknot Construction

See 2 in action at:
https://www.youtube.com/watch?v=kQpTj5Hh89M
https://www.youtube.com/shorts/kG2VVz8ND6w

For more information about Polyknots and Polylinks see: https://sites.google.com/view/polyknotsandpolylinks/Welcome-to--The-Polyknot-and-Polylink-Library?pli=1

To see all the construction systems, sets, and kits visit: https://www.thingiverse.com/APC5/collections/42405859/things

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 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.

In addition, I added the Triangles C Hinges (Long and Short versions). With these two parts and the polygons you will be able to build all the Escher Polyknots!

Source: https://www.printables.com/model/482128-archipanels-make-your-own-polyhedra