Yes, it does.
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A lower-case 'h' has rotational symmetry. An upper-case 'H' also has reflective symmetry.
Two.
There are 10 letters in the alphabet that achieve rotational symmetry when displayed in their capital form. These letters: A, H, I, M, O, U, V, W, X, and Y.
H
The letters: I O H X o x all exhibit bilateral symmetry and rotational symmetry, with O and X exhibiting it in both upper and lower case.