Abstract: An integrated dimorphic rod and joint truss structure which is erected simply and quickly from a collapsed to a high strength, rigid or semi-rigid three-dimensional form using interconnected square base members and quadrilaterals which are erected from a collapsed position on the base members to an upright and then to a skewed or twisted position creating adjacent right square pyramids having vertices joined in squares. The right square pyramid shapes produced have a high load-bearing capacity and may be arranged to produce flat, arched, vaulted or compound three-dimensional structures useful in comprising and supporting roofs, floors or portions of other structures.