SOLUTION: What is the relationship between the number of vertices, the number of faces and the number of edges of a triangular prism and a pyramid whose base is a regular triangle?

Question 1004695: What is the relationship between the number of vertices, the number of faces and the number of edges of a triangular prism and a pyramid whose base is a regular triangle?
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
What is the relationship between the number of vertices, the number of faces and the number of edges
of a triangular prism and a pyramid whose base is a regular triangle?
---------------------------------------------------------------

For a triangular prism: F - E + V = 5 - 9 + 6 = 2,
    where F is the number of faces, E is the number of edges and V is the number of vertices.

For a triangular pyramid: F - E + V = 4 - 6 + 4 = 2,
    the same number as for a triangular prism.

It is the consequence of the famous Euler's theorem.

The fact that the base is a regular triangle, is not essentially important.
The relation is valid for many polyhedra that are surfaces of convex solid bodies. See the referred Wikipedia article.

RELATED QUESTIONS
write an equation using f for the number of faces, e for the number of edges and v for... (answered by richard1234)

in a cube, how does the number of faces compare to the number of edges? what I came up... (answered by BrittanyM)

What is the relationship of the number of edges and the number of the vertices in a... (answered by richard1234)

find the number of vertices, faces, and edges for the regular hexagonal... (answered by alicealc)

A polyhedron with 6 vertices and 12 edges is shown below. What is the total number of... (answered by AnlytcPhil)

What is the product of the edges , vertices,and faces of an open cuboid (answered by ikleyn)

A pyramid with a polygonal base has 24 edges. The number of faces it has... (answered by ikleyn)

Let P be a polyhedron. The dual polyhedron of P is a polyhedron Q which satisfied the... (answered by ikleyn)

Euler's formula, V-E+F=2, relates the number of vertices V, the number of edges E, and... (answered by fractalier,stanbon)