The Supreme Order of the Rectangle (PROSE: The Plotters) was a mystical secret society created by Faction Paradox (PROSE: Interference - Book One) and noted for their usage of the rectangle, mostly as a symbol on their daggers. Bob Hay was a member of this brotherhood; when he learned that the First Doctor could travel through time, he labelled him as "Behemoth of the Supreme Order of the Rectangle".
The Order played a vital role in the Gunpowder Plot in November 1605. First devised by the Grand Council in Grammont, France, the plot aimed to plunge Europe into chaos. This was to be achieved by sending Bob Hay to London to manipulate both Protestant and Catholic sides, but following interference of the First Doctor, eventually culminating in Bob Hay himself being arrested as he was about to blow up parliament, with Sir Robert Cecil framing him as Guy Fawkes. (PROSE: The Plotters)