What is the number of vertices in an octahedron?

An octahedron is a type of polyhedron that has eight triangular faces. To determine the number of vertices in an octahedron, it's helpful to visualize or consider its structure. An octahedron can be imagined as two pyramids joined at their bases.

When you analyze it, you'll see that it has a total of six vertices. These correspond to the apex of the two pyramids (the top vertex of one and the bottom vertex of the other), along with the four vertices that form the base square between the two pyramids.

Using Euler's formula for polyhedra, which states that V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces, also helps confirm this. An octahedron has 8 faces, 12 edges, and plugging these into the formula gives us V = E - F + 2, leading to 6 vertices.

Thus, the correct answer, indicating that an octahedron contains six vertices, aligns with the geometric rules and structures involved in defining this shape.