Exploring twin-edged polyhedral links and knots

This paper presents ways of making stripped-back polyhedra inspired by Marleen Hartog’s knitted cubes. They are already-discovered topologies made from cane trained over 3D printed jigs and include Platonic solids, woven tessellations and cylinders. They are associated with Holden’s Orderly Tangles. The work sheds light on, emphasizes, assesses as a group, and realizes in human-scale objects described in other papers. This makes it complimentary Mallos’s work (2017) representing DNA nanostructures at visible scales. This paper links Marlene Hartog’s art with science and mathematics, including that of DNA nanostructures. The cane Platonic solids have spherical geometry where vertices become flat nodes. They are patterned, sometimes symmetrical topological links and knots with edge and node crossings. Further discovery could include constructing patterns, tessellations, and cylinders which have been identified but not built: models which could be made in classrooms to do and enjoy maths.