Rigidly foldable origami tubes with open ends have been reported in the past. Here, using a mechanism construction process, we show that these tubes can be used as building blocks to form new tubes that are rigidly foldable with a single degree-of-freedom (SDOF). A combination process is introduced, together with a possibility of inserting new facets into an existing tube. The approach can be applied to both single and multilayered tubes with a straight or curved profile. Our work provides designers great flexibility in the design of tubular structures that require large shape change. The results can be readily utilized to build new structures for engineering applications ranging from deployable structures, meta-materials to origami robots.