Isotropic Herringbone

While there are simple isotropic fabrics that fit this description, they all seem to do a terrible job of locking the fibres in place - a basic and important feature of triaxial fabrics.

After considerable experimentation, probably the best approach I have found to this so far is to construct a fabric made of multiple small patches of the above fabric - with the weft travelling in different directions in the various patches - as follows:

First herringbone triaxial weave (isotropic variant)

This technique produces rotational symmetry at considerable expense in terms of translational symmetry - and several other desirable properties of the fabric.

The fabric may look like a random mess, but it is composed of tesselated identical hexagons, each of which is rotationally symmetric about its centre point. You may be able to see the hexagonal pattern if you squint at the fabric.

The size and shape of the patches could - in principle - be varied.