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In summary, the polygon extension theorem states that any two polygons can be continuously extended or connected to form a larger polygon. A convex polygon has all interior angles less than 180 degrees, while a concave polygon has at least one angle greater than 180 degrees. A polygon cannot be both convex and concave. A regular polygon has all equal sides and angles, while an irregular polygon has different lengths and measures. A polygon cannot have an infinite number of sides, but the number of sides can approach infinity, such as in the case of a circle.

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Something along the line of the Von Neumann paradox, but without the paradox part?

Yes, any two polygons can be continuously extended or connected to form a larger polygon. This is known as the polygon extension theorem and it states that if two polygons share a side, then the two polygons can be extended or connected to form a larger polygon.

A convex polygon is a polygon in which all of its interior angles are less than 180 degrees, while a concave polygon has at least one interior angle that is greater than 180 degrees. In other words, a convex polygon has no "dents" or indentations, while a concave polygon has at least one "dent".

No, a polygon cannot be both convex and concave. A polygon is either convex or concave, depending on the measure of its interior angles. If a polygon has at least one interior angle greater than 180 degrees, then it is concave. If all of its interior angles are less than 180 degrees, then it is convex.

A regular polygon is a polygon in which all of its sides and angles are equal, while an irregular polygon has sides and angles of different lengths and measures. In other words, a regular polygon is symmetrical, while an irregular polygon is not.

No, a polygon cannot have an infinite number of sides. A polygon is a closed shape with finite sides and angles. However, the number of sides can be very large, approaching infinity, in the case of a circle which can be considered as a polygon with an infinite number of sides.

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