The purpose of this page is to show that new
polyhedrons can be obtained similar to those presented on the page of ‘Literka’
Polyhedrons Built of
Rhombuses by changing angles of rhombuses (which are faces of polyhedrons).
Example 1. Take a
polyhedron with 12 congruent rhombuses (see Polyhedrons Built of
Rhombuses). Let us try to construct a similar polyhedron starting with
rhombuses having angles 60 degrees and 120 degrees. Our construction will end up
with a polyhedron with 12 faces: 8 rhombuses with angles 60 and 120 degrees and
4 squares. Let us show a picture of this polyhedron:
Example 2. Take a polyhedron built of 20
rhombuses (see Polyhedrons Built of
Rhombuses). Let us remind that this polyhedron has 10 faces being rhombuses
with angles 60 degrees and 120 degrees and 10 faces being rhombuses with angles
75 degrees and 105 degrees. It appears that we can change angles of these
rhombuses to obtain a polyhedron with congruent rhombuses. Let us present a
picture of this polyhedron:
Let us consider a rhombus W of any face of this
polyhedron. Let us take a polyhedron V (presented on the page Polyhedrons Built of
Rhombuses) built of 30 congruent rhombuses. Each face of V is a rhombus with
the same angles as W. That is why we can say that a polyhedron built of 20
congruent rhombuses can be received from V by removing 10 faces (and joining
obtained 2 parts). Finally, let us show how to construct a rhombus W. The
following picture explains this construction:
The yellow polygon is a regular pentagon, the red
rhombus is a face of a polyhedron built of 20 or 30 rhombuses. There are the
following relations: (*) the length of PR is the same as length AB
(length of side of pentagon) (*) the length of QS is the same as
CE.
