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The type of truss that is not recognized within standard roofing structures is the square truss. While trusses are essential components in roof construction, serving to distribute weight and provide structural support, the square truss does not specifically refer to a common design used in roof framing.

In roofing terminology, each type of truss has specific characteristics and purposes. For example, a mono pitch truss features a single sloped surface, allowing for simpler roof designs often used in lean-to structures. The double pitch profile truss, also known as a gable truss, consists of two sloping sides that meet at a peak, which is a common style in residential buildings. The Fink truss, characterized by its web configuration that resembles an "A" frame, is widely used for its efficient strength and lightweight construction.

In contrast, while there are truss designs that might be square or incorporate square shapes, the square truss is not a standard term recognized in the context of roof trusses, making it the correct choice in this instance.