Although I didn't weave this fabric, I wanted to include a write-up of it's making in order to add to the body of knowledge about it on the internet. The weaver, Toby, very kindly made a video explaining a little about it which you can find here.
Techniques involved: Weaving on a 4 shaft loom.
Tools used: 4-shaft table loom.
The find is called Jorvik 1336 and can be read about in the York Archaeological Trust publication, Textiles, Cordage and Raw Fibre from 16-22 Coppergate by Penelope Walton. As Priest-Dorman mentions, there is a weaving draft included but it's actually simpler to weave if you turn the diagram on it's side. We have no way of knowing which thread was warp and weft in this fabric but in order to weave it on a four shaft loom Toby followed Priest-Dorman's advice.
The original was a vegetable fibre - most likely linen - and was found with some other small pieces of fabric. honeycomb weave structure is not widely known amongst Viking finds, though there have been others, so this was an unusual bit of fabric. Walton has this to say about it's origin:
Since several other patterned linens, particularly weaves based on the same 2/1 structure (Fig. 172), have been found in the Frankish row-graves of West Germany, the Rhineland seems a possible source for this group of textiles.
The fabric woven for me is most obviously different in that it is wool. This choice was for multiple reasons, including that I had lots of wool thread to hand and also that Toby has experience of weaving wool but hasn't woven linen before.
Queries: This being quite an unusual weave in terms of how often it is found in a 9th/10th century context makes me wonder if there is any likelihood that it was ever woven in wool. There's also the eternal mystery of what this small, carbonised fragment was originally a part of.
Summary: Having fabric of the right structure and quality is something I am really hoping to move my kit towards and this feels like a great first step.