Answer
See the explanation
Work Step by Step
I can describe how to design a polygonal mesh representing a rectangular solid using a traditional rectangular coordinate system:
1. **Identify Vertices**: A rectangular solid has 8 vertices. Each vertex is represented by a set of three coordinates (x, y, z) in the 3D space.
2. **Assign Coordinates**: Assign coordinates to the vertices based on the dimensions of the rectangular solid. Let's say the length, width, and height of the rectangular solid are denoted by L, W, and H respectively.
The vertices of the rectangular solid can be represented as follows:
- Vertex 1: (0, 0, 0)
- Vertex 2: (L, 0, 0)
- Vertex 3: (L, W, 0)
- Vertex 4: (0, W, 0)
- Vertex 5: (0, 0, H)
- Vertex 6: (L, 0, H)
- Vertex 7: (L, W, H)
- Vertex 8: (0, W, H)
3. **Connect Vertices to Form Faces**: Use the coordinates of the vertices to form faces by connecting them in the correct order. For a rectangular solid, there are 6 faces: front, back, top, bottom, left side, and right side. Each face is represented by a set of vertices connected in a specific order.
4. **Sketch Representation**: I can't draw directly, but you can visualize the rectangular solid by connecting the vertices in the correct order to form the faces. Each face will be a quadrilateral formed by connecting four vertices.
Here's a text representation of the sketch:
```
8--------7
/| /|
/ | / |
4--|-----3 |
| 5-----|--6
| / | /
|/ |/
1--------2
```
Each vertex is labeled with its corresponding number, and the edges connecting them represent the edges of the rectangular solid.
