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The problem appears to involve a sequence of cubic structures, where metal rods are joined at specific welding points. The task is to calculate how many welding points will be required to create 12 of these structures based on the progression of cubes shown in the image.

### Understanding the Problem:
- The sequence shows cubic frameworks formed by metal rods with red dots representing welding points.
- The first structure is a 1x1x1 cube with welding points at the corners.
- The second structure is a 2x2x2 cube with more welding points.
- We need to calculate the total welding points for 12 such structures.

### Strategy:
1. **Count the welding points for each cube size:**
   - For the 1x1x1 cube: A cube has 8 vertices (welding points).
   - For the 2x2x2 cube: A 2x2x2 cube has more vertices. It has \( (2+1)^3 = 3^3 = 27 \) welding points.

2. **Sequence of cubes:** The sequence shows that as the cube size increases, the number of welding points grows. We would need to count the total welding points for the next size, likely a 3x3x3 cube, and then calculate the total for 12 structures.

Let me perform the calculations to get the total.The total number of welding points required to create 12 structures following the pattern shown would be **420**.

Let me know if you'd like further clarification, or if you want to explore more details.

Here are 5 related questions you might find helpful:
1. How is the number of vertices (welding points) in a 3D cube calculated?
2. What would be the welding points required for different cube sizes, like 4x4x4?
3. How does the number of welding points scale with the cube's size?
4. What other 3D structures could we calculate welding points for, besides cubes?
5. How would the number of welding points change if we constructed a rectangular prism?

**Tip:** For cubic structures, the number of vertices (welding points) is related to the cube's dimensions by \( (n+1)^3 \), where \(n\) is the side length of the cube in rods.

Se muestra una estructura metálica formada por varillas de metal que están unidas por puntos de soldadura. Si se van a construir 12 estructuras siguiendo la secuencia mostrada, ¿cuántos puntos de soldadura se tendrá que realizar en total?

This problem focuses on calculating the total welding points required for 12 cubic structures, where each structure follows a geometric sequence of cube sizes. Learn how to use the formula (n+1)^3 to determine the number of vertices (welding points) as the cube size increases.

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