Orderly Tangles

[otiososmanus]

It was Paper Polylinks by George W. Hart

that I first made reference to on the start of this journey.

And Hart provided a host of way markers throughout.

[otiososmanus]

So this was the first orderly tangle construction I made during the covid lockdown. It's the Four Triangle Polylink. (Actually, this is one of two types of four triangle polylink - the better known one.) As this polylink is thought of as being derived from the tetrahedron, that Platonic solid is considered the structure’s “parental polyhedron.”

[otiososmanus]

The orderly tangle called the Four Triangle Polylink, in its pure form, is made up of interlinking hollow polygons whose central open space is a triangle exactly half the height of the whole shape. The formulation of this polylink is usually explained as the rotation of each face of a tetrahedron by 30 degrees and then the "translation" of each one into the centre of the space that would have been occupied by the polyhedron.