V-e+f for a hexagonal prism

Answer 1

The Euler characteristic formula for any polyhedron, including a hexagonal prism, is given by:

V - e + f = 2

where:
V is the number of vertices (corners),
e is the number of edges, and
f is the number of faces.

A hexagonal prism has 2 hexagonal faces (top and bottom) and 6 rectangular faces (sides), for a total of 8 faces.

The number of vertices can be calculated by summing the number of vertices for each face. The hexagonal faces each have 6 vertices, and the rectangular faces each have 4 vertices. Since there are 2 hexagonal faces and 6 rectangular faces, the total number of vertices is 6 + 6 * 4 = 30.

The number of edges can be calculated by summing the number of edges for each face. The hexagonal faces each have 6 edges, and the rectangular faces each have 2 edges. Since there are 2 hexagonal faces and 6 rectangular faces, the total number of edges is 6 + 6 * 2 = 18.

Plugging these values into the Euler characteristic formula, we get:

30 - 18 + 8 = 20

So the Euler characteristic (V - e + f) for a hexagonal prism is 20.