| Summary: | In 2015, the author developed a new origami technique, called PJS technique (where PJS stands for “pleat and join strips”), by which we can construct polycubes, that are polyhedrons composed of elementary cubes, called units, connected face to face. Each strip, pleated in squares, has to cover four faces of a tower of stacked units, called a segment, having as length the number of units that form the tower. Each unit is composed by weaving together three paper strips in the three spatial directions and the length of each strip depends on the length of the segment in each respective direction. The PJS technique allowed the author to build, at the end of 2016, the first specimen of a level-4 origami Menger sponge and three yeas later, the first level-3 complement model. In this paper, we give a formula to compute the number of segments that make up a level-<i>n</i> Menger sponge complement in all directions and consequently, the number of modules needed for each length to build this polycube with the PJS technique.
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