No but capital H is a symmetrical letter
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B,C,c,D,E,H,I,K,l,M,N,O,T,U,V,v,W,w,X,x,Y
Yes. It has vertical, horizontal and diagonal planes of symmetry
Usually the letter h represents height.
Pentagons can be symmetrical, but are not always so.
The space it occupies isn't symmetrical.