The sum of the interior angles of a polygon is given by the formula:

$S_{\text{interior}} = 180(n-2)$

where $n$ is the number of sides of the polygon.

The sum of the exterior angles of any polygon is always $360^\circ$, regardless of the number of sides. So, the sum of the exterior angles is:

$S_{\text{exterior}} = 360^\circ$

According to the problem, the sum of the interior angles is twice the sum of the exterior angles. Therefore, we can set up the following equation:

$180(n-2) = 2 \times 360$

Simplifying the equation:

$180(n-2) = 720$

Divide both sides by 180:

$n - 2 = 4$

Add 2 to both sides:

$n = 6$

Thus, the polygon has 6 sides. It is a regular hexagon.

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Would you like more details or have any questions on this solution?

Here are some related questions to explore:

1. How do you calculate the sum of the interior angles for any polygon?
2. What is the sum of the interior angles for a decagon (10-sided polygon)?
3. How do the interior and exterior angles of a polygon relate to each other in general?
4. What is the measure of each interior angle in a regular hexagon?
5. What are the applications of polygons with different numbers of sides in geometry?

Tip: For any regular polygon, the exterior angle is simply $\frac{360^\circ}{n}$, where $n$ is the number of sides.