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Convex polyhedrons built |
There are few types of polyhedrons for which all faces are equilateral triangles. This shows that a polyhedron may have all the same faces of regular polygons, but polyhedron itself is not regular.
Type 1. Polyhedron of 16 faces.
We list this type first, because a picture of it is above. It is
not a regular polyhedron (Plato polyhedron), because some vertices are common
points of 4 edges and some of them are common points of 5 edges. There is a
special page of ‘Literka’ devoted to this polyhedron. Visit example of a polyhedron.
Type 2. Polyhedron of 10 faces.
This polyhedron consists of two polyhedrons, which are considered
on the page of ‘Literka’ ICOSAHEDRON.
Each of the pieces was called
‘UFO’, because of theirs shape. Visit this page to see pictures and remarks.
Type 3. Polyhedron of 6 faces.
This is a polyhedron consisting of two regular tetrahedrons. However
this polyhedron is not regular (is not a Plato’s polyhedron). In fact, it is
the simplest polyhedron, which has all faces of the same copies of a regular
polygon and it is not a regular polyhedron. We may see that some vertices are
common points of 4 edges and some of them of 3 edges.
We do not present pictures for next
types of polyhedrons, because they are Plato’s polyhedrons. See a page of
‘Literka’ Plato's
Polyhedrons, where these pictures are included.
Type 4. Regular tetrahedron. (Plato’s
polyhedron)
This is the simplest kind of considered polyhedrons. (Picture on
the page mentioned above).
Type 5. Regular octahedron. (Plato’s
polyhedron)
This polyhedron consists of 2 pyramids. (Picture on the page
mentioned above).
Type 6. Regular icosahedron. (Plato’s
polyhedron)
As before, a picture is included on the page devoted to Plato’s
polyhedrons. However, for this type there is a special page of ‘Literka’ ICOSAHEDRON describing
this type.