How many faces does a pentagonal pyramid have?
If you are referring to a pyramid with a pentagonal base and triangular sides, the answer is six.
If you are referring to a regular polyhedron for which all sides are regular pentagons of the same size, the answer is twelve. That figure is called a dodecahedron.
See http://en.wikipedia.org/wiki/Dodecahedron
for an illustration.
To find the number of faces a pentagonal pyramid has, it is useful to understand the shape of the pyramid.
A pentagonal pyramid has a pentagonal base and triangular sides that meet at a common vertex. The base of the pyramid is a polygon with five sides, so it has five faces. Additionally, each of the five triangular sides of the pyramid counts as one face. So in total, a pentagonal pyramid has six faces.
However, if you are referring to a regular polyhedron with all faces being regular pentagons, then it is called a dodecahedron. A dodecahedron has 12 faces, each of which is a regular pentagon.
To summarize:
- A pentagonal pyramid has a pentagonal base and five triangular sides, resulting in six faces.
- A regular dodecahedron is a polyhedron with 12 regular pentagonal faces.