Virginia West's Weaver's Wearables shows a triangular shawl, which she calls a triangular stole, woven on a regular 45 inch wide horizontal loom.
The fad these days is to weave a triangular shawl on a dedicated triangular loom. That sort of loom appeals to some folks. It repels me because of its style, size, and single purpose. I suspect that even the shawl it produces is not my taste.
At any rate, I found it interesting that you can get the same product using different equipment. You warp, then starting at one edge you clip warp threads one by one to use for weft, creating a bias selvedge and bias fabric when worn.