# Category Archives: knots

## Icosahedral Symmetry as a Decorative Knot

The decorative knots to be discussed here are those which are tied with one or more cords that may be repeated through several plies. These sorts of knots can be represented by self-intersecting loops on the plane, set up so that no more than two loops intersect at any single point. One generates a tying diagram from such by picking which of the two paths are uppermost at each intersection point. While this could be done more arbitrarily, for the knots discussed here the paths will be selected so that each path alternates over and under as in:

My eventual objective here is to tie a knot with approximate dodecahedral or icosahedral symmetry. Let’s begin with a line drawing that has the right symmetry. Flattened out to the plane, the dodecahedron looks like the following planar graph:

But this is not in the form we need; it is not in the form of a collection of loops. The basic problem is that, as a graph, there are three edges meeting at each vertex.

Filed under knots

## A new way to tie an old knot

The tying diagram Ashley gives for ABOK #2217 has a 4-fold axis of symmetry:

Tying a knot according to a diagram like this is quite time consuming. One must redraw the diagram by photocopying to the size needed. And in tying the knot, one pins the rope to the diagram. This is a pain because the rope moves around, the pins come out, etc. And the pins can damage the appearance of the rope.

In this post I give an alternative method of tying this knot, and several others like it, that is easier to set up, is much faster for each knot, and uses cheaper materials. Rather than an expensive cork board, we will use a 2×2 and build the knot as if it were a sort of Turk’s Head knot, on a cylindrical of square form.