MATHEMATICS AND ORIGAMI

Mathematics and Origami

Present Fig. 2 is the folding diagram of the wedge, once we have available all the in-

formation needed (see Point 18.14.5). To note that the three angles in D are pentagonal of 108º.

18.14.7 THE IRON CROSS

Also known as IRON ROSE, is a complement macle. The pyrite often crystallises in

that mode.

To study it we shall start with the pentagonal-dodecahedron of Fig.1 to be associated to

Point 18.6.1: here, AB will be what was called there great diagonal D; obviously, BC is the side

l of the polyhedron, and CD is one of the facial pentagon ́s diagonals then named d.

In Point 18.6.1 we saw that D – d = l, which is the peculiar property we are going now

to take advantage of. It will permit us to draw Fig. 2 that consists of a set of trirrectangular

crosses of these characteristics:

• Its center O coincides with the dodecahedron ́s.


• The great arms type AB have the measure of AB (Fig. 1; the great diagonal AB mentioned
  before).


• The segments type DC measure as much as the diagonal DC of Fig. 1; they will determine a
  cube type CDCD (see Fig. 3).


• The small crosses type BCCCCC have their arms made by segments half of the side BC in
  Fig. 1.

3 4

C B

C

C

C

D

C

D

C

C