MATHEMATICS AND ORIGAMI

Mathematics and Origami

18.2.4 HEXAGONAL PYRAMID

The folding process beginning in Fig. 1, is self-explanatory. Fig. 5 shows how to cut along
the solid line to get Fig. 6. After folding the latter, we obtain pyramid 7.
As said in Point 18, a hexagonal polyhedral angle must be constructed with plane angles
smaller than 60º. Fig. 9 shows a lateral face whose altitude is twice that of the equilateral triangle
having a side equal to the base hexagon (see Fig. 4). This means, in our case, that the apothem of
the pyramid is double of the base ́s apothem. Bearing this in mind we can figure out angles α and β:

60 º

2

1

α=arccos = ; 32 , 204228 º

2

3

2

= 2 arctg^2 =

l

l

β

1

2

4

6

3

5

9