Equilateral triangles
-Tetrahedron
3 faces at each vertex
-Octahedron
4 faces at each vertex
-Icosahedron
5 faces at each vertex
Squares
-Cube (hexahedron)
3 faces at each vertex
Pentagons
- Dodecahedron
3 faces at each vertex
Here are short explanations of some Polyhedra…
Tetrahedron
This is the simplest of all the polyhedra. It uses the least number of faces to enclose any three-dimensional space. The polygon that makes up these faces is also the simplest polygon. Tetrahedron has 4 vertices, 6 edges and 4 faces.
Hexahedron
Hexahedron is the most common polyhedron. A hexahedron is a polyhedron with six faces. It is often called cube. The thing about the cube (hexahedron) is that all the other regular polyhedra can be derived from taking cuts across the cube to form a tetrahedron first, and accross the tetrahedron to give an octahedron, and so on.It has 8 vertices, 12 edges, and 6 faces.
Octahedron
Octahedron is made from placing two square based pyramids base to base. It has eight faces – Octa. It is interesting that with this polyhedron no matter what way you look at the solid the same configuration of the faces that make up the solids will always be seen. Octahedron has 6 vertices, 12 edges and 8 faces; 3 edges per faces and 4 per vertex.
Icosahedron
Icosahedron has 12 vertices, 30edges, and 20 faces.
Dodecahedron
It is with this polyhedron that the production of regular polyhedra ends. It has 20 vertices, 30 edges and 12 faces.
There are Archimedean solids:
, , , , , , , ,
Truncated Icosahedron (soccer ball/60-carbon fullerene/bucky ball)
Truncated Icosahedron is one type of polyhedron we chose. It has many “names”, such as 60-carbon fullerene, bucky ball and soccer ball. It is because this polyhedra is almost round and looks like each of them. For example, it is often called soccer ball because it looks like a soccer ball. However, it is different. In this model all the surfaces of the faces are flat, unlike the spherical surface of a soccer ball. It has 32 faces, 90 edges and 60 vertices. 12 faces are pentagons that are replacing the twelve original vertices of the icosahedron. The other twenty faces are hexagonal.
Definition
A polygon is said to be regular if it has equal sides and equal angles.
A polyhedron is said to be regular if its faces are regular polygons and its corners are regular solid angles. Also equal faces and equal angles.
References
.
http://www.ul.ie/~cahird/polyhedronmode/hexahedr.htm - 27k