A collapsible structure comprising a collapsible support structure having a flexible covering disposed thereon. The support structure comprises a plurality of pole members that emanate from an upper assembly. The upper assembly has first and second hub members that, when brought into abutting contact with each other, cause the structure to assume a fully constructed configuration but when separated from each other allow the structure to become collapsed. In many embodiments, the structure can be converted from its constructed configuration to its collapsed configuration substantially with the use of a single hand. In some embodiments, 2 or more of the collapsible structures may be joined together to form a multi-unit structure. These collapsible structures may include decorative markings on the flexible cover, especially in embodiments intended for use by or entertainment of children.