MATHEMATICS AND ORIGAMI

Mathematics and Origami

Fig. 2 is the same Fig.1 transformed by revolving the latter about OX a dihedral angle of
α = 40º (corresponding to an obtuse angle of 140º). To draw Fig. 2 we have to pursue the steps
that follow.

In that revolution (Fig. 2), AB is a parallel to OX just like its image A ́B ́. Hence, for
any position during rotation always is AA ́= BB ́. Then triangles APA ́ and BOB ́ are congru-
ent for their three sides are, respectively, equal. This entails that Ang. APA ́ = Ang. BOB ́.
These angles measure the values of equal dihedral angles in (- XO) and (XO) for they are re-
spectively in normal planes to (- XO) and (XO).

Let ́s seek now the other dihedral angles in OD and OE that are congruent because of
symmetry. We can see in Fig. 2 that wanted angle BCN is the measure of those dihedral angles.

O

D

A B

C

N

• X X

P

E A ́

B ́

1

3