The present invention provides for the first time a foldable structure comprising a resilient frame and a coiling-assist assembly for facilitating coiling the resilient frame while folding. The coiling-assist assembly comprises a releasable grasp coupled to the resilient frame at a pre-determined first location. The releasable grasp temporarily holds the resilient frame in a first folding configuration, whereby the pre-determined second location of the resilient frame is diametrically opposed to the pre-determined first location of the resilient frame.