An octagonal prism has a total of 10 faces, 24 edges, and 16 vertices.
To understand this, let’s break it down:
- Faces: An octagonal prism consists of 2 octagonal bases and 8 rectangular lateral faces. So, the total number of faces is 2 (octagonal bases) + 8 (rectangular faces) = 10 faces.
- Edges: Each octagon has 8 edges, and since there are 2 octagonal bases, that contributes 16 edges. Additionally, there are 8 edges connecting the two octagons (one edge for each vertex of the octagon). Therefore, the total number of edges is 16 (from the bases) + 8 (connecting edges) = 24 edges.
- Vertices: Each octagon has 8 vertices, and with 2 octagonal bases, the total number of vertices is 8 (from one base) + 8 (from the other base) = 16 vertices.
In summary, an octagonal prism has 10 faces, 24 edges, and 16 vertices.