Mathematics and Origami3- All the diagonals will be mountain fold except those affected by a module
change (see later). Therefore these diagonals should be pre-folded within the
great rectangle in order to ease the process.
4- Cut 10 strips; join them in such a way that two extreme diagonals will overlap
keeping all the diagonals as mountain folds. Hence we have produced a strip
made out of 90 isosceles triangles.
5- To facilitate the process, begin with half of the joined strips, wind up the poly-
hedron and add new strips when needed.
6- The diagonals in the strip will become the sides of the polyhedron, and the bases
of the isosceles triangles will be the diagonals of its pentagonal faces.
7- From one extremity of the great strip, build an enclosed module having 5 + 5
bases of the corresponding isosceles triangles. Glue the module ́s beginning and
end to each other making sure that first and last diagonal coincide. In Fig. 2 we
can see that module showing those bases set off. It has the vertices ABCDE
common with the corresponding ones in Fig. 3.
8- Each one of the modules is a part of the dodecahedron and is determined by two
sections parallel to the base of the polyhedron: that base changes as the paper
strip is wound around.
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