June 26, 2019
A polyhedron is a three dimensional region of space bounded by polygons.
The faces of a polyhedron are each of the two dimensional polygons that border the polyhedron.
The edges of a polyhedron are the sides of the faces of the polyhedron. Two faces have an edge in common.
The vertices of a polyhedron are the vertices of each of the faces of the polyhedron. Three faces coincide with the same vertex.
The dihedral angles are formed between two faces of all neighboring polygons.
Polyhedral angles are formed by three or more faces of the polyhedron and have a common vertex.
The diagonals of a polyhedron are the line segments joining two vertices not belonging to the same face.
It is verified that in all convex polyhedra:
No. of faces + No. of vertices = No. of de edges + 2.
In a convex polyhedron, a straight line can only penetrate the surface in two points.
In a concave polyhedron, a straight line can pentrate the surface in more than two points.
A regular polyhedron is composed of angles and faces (regular polygons) that are all equal.
The platonic solids are convex regular polyhedra. There are exactly five types of platonic solids:
An irregular polyhedron is defined by polygons that are composed of elements that are not all equal.
Polyhedron of 4 faces.
Polyhedron of 5 faces.
Polyhedron of 6 faces.
Polyhedron of 7 faces.
Polyhedron of 8 faces.
Polyhedron of 9 faces.
Polyhedron of 10 faces.
Polyhedron of 11 faces.
Polyhedron of 12 faces.
Polyhedron of 20 faces.