The Asokan stone pillars are stone columns erected by Emperor Ashoka of the Mauryan dynasty during his reign in the 3rd century BC in India.

Option 1: These pillars are indeed highly polished, which reflects the sophisticated methods and techniques used during the Mauryan period. So, this statement is correct.

Option 2: The term `monolithic` refers to a stone structure that is made out of a single piece of stone. The Asokan pillars were indeed made from a single piece of stone, so this statement is also correct.

Option 3: The shaft of the pillars is described as tapering in shape, which means it gradually becomes thinner towards one end. This design is consistent with the known structure of the Asokan pillars. Hence, this statement is correct.

Option 4: This statement is incorrect because the Asokan pillars are not parts of architectural structures. They are freestanding and were often erected at important religious and political sites to disseminate Ashoka`s policy of dharma. Some pillars had edicts carved on them, reflecting Ashoka`s governance and law.

So the provided answer is correct. The Asokan pillars are not part of architectural structures.