The base of a prism is a octagon. All its other faces are rectangle. What is the name of such a prism ?

Answer

To solve the question about the prism with an octagonal base, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Base Shape**: The base of the prism is given as an octagon. An octagon is a polygon with 8 sides.

**Hint**: Remember that the number of sides in a polygon determines its name. For example, a triangle has 3 sides, a square has 4 sides, and an octagon has 8 sides.

2. **Understand the Structure of the Prism**: A prism is defined as a solid shape that has two parallel bases that are congruent (the same shape and size) and rectangular faces connecting the corresponding sides of the two bases.

**Hint**: Think about how a prism is formed. It is like stacking two identical shapes on top of each other and connecting them with rectangles.

3. **Determine the Faces of the Prism**: Since the base is an octagon, the prism will have two octagonal bases. The other faces connecting these bases will be rectangles.

**Hint**: Count the number of faces. For an octagonal prism, there are 2 octagonal faces and 8 rectangular faces (one for each side of the octagon).

4. **Count the Vertices and Edges**:
- **Vertices**: Each octagonal base has 8 vertices. Since there are two bases, the total number of vertices is 8 (top base) + 8 (bottom base) = 16 vertices.
- **Edges**: Each octagonal base has 8 edges, and there are 8 additional edges connecting the corresponding vertices of the two bases. Thus, the total number of edges is 8 (top base) + 8 (bottom base) + 8 (connecting edges) = 24 edges.

**Hint**: Remember that each vertex on the top base connects to a vertex on the bottom base, forming vertical edges.

5. **Name the Prism**: Since the base of this prism is an octagon and all other faces are rectangles, the name of the prism is an "Octagonal Prism".

**Hint**: The name of a prism is derived from the shape of its base. If the base is an octagon, it is called an octagonal prism.

### Final Answer:
The name of the prism with an octagonal base and rectangular faces is an **Octagonal Prism**.