Thank you to Richard Hunter for reminding us of the "infamous" Jackstone. I find it difficult to approve of this baleful epithet. If it is difficult to fold, it is not nearly a difficult as many folds today that folders revel in. In fact I was already familiar with the Jackstone. More than that, I successfully managed to fold it from the photographic instructions that appeared in the Origamian. I've never folded anything since!
The Jackstone is not, of course, modular folding. Folding the regular polyhedra and other not so regular ones has fascinated not only mathematicians, but also ordinary people from time immemorial and efforts have for long been made to reproduce them. The earliest techniques were paper constructional methods using multiple pieces and glue. Later cut-out "nets" were used, in which the polyhedron was "unfolded" so that each face remained connected to one of its neighbours, but the whole made to lie flat. Another method was to use long strips of paper woven together to make the polyhedra. ("Woven Polyhedra".)
The Jackstone was a single piece of paper folded without cuts to form the model. "Jackstone" was merely was Jack's own name for a stellated cube. He gave it the name from the game of Jacks which children play, in which they throw up a small ball and grab the requisite number of jacks before catching the ball again. It is still popular in many parts of the world and probably has various names and rules. The further challenge arising our of the Jackstone was to fold a kind of three dimensional Greek Cross, being a core cube with a cube on each face. I have never discovered whether anyone actually achieved this, but it should not be too difficult for folders experienced in box-pleating.
The first attempts in _origami_ to fold polyhedra used the same single-sheet method as Jack's Jackstone. I have even found examples of "proto-polyhedra" by Yoshizawa in, of all places, the original longer hard-backed version of "The World of Origami". This book was published in 1965, but Yoshizawa's creations must have been much earlier than this, before tensions between the two folders developed. Bennett Arnstein was an early American investigator with his book, "Modular Origami", which was published in 1968 and now a great rarity.
The method of using not a single sheet, but several or many sheets folded into identical modules to form polyhedra apparently began tentatively in the late 1950s, although there were early traditional examples in Japan dating back to the 18th century. Some Kusudamas took this form. The first origami modules created solid-faced polyhedra, like the cubes of Lewis Simon. Various modules were devised, but it was the module that Toshie Takahama used for her famous jewel, (which seems to have appeared around 1960s) that initiated a craze for folding polyhedra. This is the module that has been attributed to Mitsunobe Sonobe. An early appearanaace of it was in one of the publications of the Sosaku Origami Group 1967, which Toshie Takahama founded with some of her friends. She had visited New York in 1965 and seen how American origami groups functioned and formed one of her own. The Jewel also appeared in her "Creative Life with Creative Origami" (1969). But whether the Sonobe module really was originated by Sonobe I have not yet been able to affirm. The books of his that I have seen are only of simple origami and do not use the module. Of course, Sonobe may have published more advanced work which I have not seen. The module attributed to Jack Skillman is a modified form of this module.
The final development was the use of modulars to form skeletal polyhedra. This emerged from the folding of modular solid polyhedra, but I have not yet dried to pin any dates on the development. Ever since then, origami exhibitions have been filled with this style of folding.
This is not intended to a connected history of modular and polyhedral origami, but it may give people some idea of the field that I am at present investigating. I have left out huge chunks, and not least the work of Tomoke Fuse. If this posting sparks off any memories or ideas, I shall, as usual, be grateful to hear of them.
David Lister Grimsby, England.
Please provide details below of any issues you may have encountered. Thank you