Is a dome house Symmetrical or Asymmetrical?

Symmetrical.

A symmetrical shape is simply one that when cut, or folded, in half, the one half can reflect the other half. So, each half looks the same, but as a mirrored reflection of the other.

On the other hand, something that is of irregular shape - which is not symmetrical in that when cut into halves in any plane at all, the pieces are not a mirror reflection of one another - is referred to as "asymmetrical".

A dome house is of symmetrical shape.