Short Words, with a Twist

In the English alphabet, the following 7 capital letters look the same after being rotated \(180^{\circ}\):

\[ H, I, N, O, S, X, Z. \]

How many different 3 letter "words" can be made from these letters such that when the word is rotated \(180^{\circ}\), the resulting word is the same?

Details and assumptions

The "words" formed do not have to be valid English words. The word SSS would be a valid word satisfying the conditions.


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