Alas, since no "behind the scenes" photos of this model have surfaced yet, fans passionately debate what was used in its construction. Spinrad himself made a comment about a "wind-sock dipped in cement," but I have to wonder why make a one time model from such a heavy material?
Like SpanglerArt, I suspect inexpensive cooking foil was used, but I (and some others) think translucent sheets of plastic, possibly scrap pieces of colored lighting "gels" were applied over the foil. If one looks at the shots of the "maw" straight on, there are some "things" that look suspiciously like strips of common transparent adhesive tape securing the "materials". I could well be wrong, but I thought I'd toss that out there.
It is pretty clear most of the shots of the "weapon" were static photos that had the cmaera pan past the image. Only when we saw the device "turn" to face the bridge crew on the main viewer did they film the model itself.