MATHEMATICS AND ORIGAMI

Mathematics and Origami

18.3 PRISMS

Let us construct an oblique equilateral triangular prism whose lateral sides form with

the base an angle β = 54,735613º (see point 18.2.2.2) having the attitude shown in Fig. 2.

Those lateral sides will measure twice the base ́s side. Under these circumstances we

have the prism of Fig. 1 whose folding scheme is Fig. 3.

18.4 TRUNCATED PRISM

Let ́s truncate the prism of Point 18.3 by a plane through A forming with the base an

angle twice the value of 90 – 54,735613. That angle is the same formed by two opposite lateral

faces in the quadrangular pyramid with vertex A. That plane divides the prism in two solids:

the upper one which is the above mentioned pyramid (already studied in Point 18.2.2.2), and

the lower one: the truncated prism as such (see Fig. 1).

Fig. 2 is the development to construct the truncated prism.

18.5 PRISM TORSION (obtention of PRISMOIDS)

When we studied the so-called SALOMONICA COLUMN in Point 17.2, we already

saw how to get the piling up of partial twists in a quadrangular prism. There we pointed out two

ways of construction: CAD and analytical. Both are basic in present study, but we shall stick to

the first.

3

A

2

A