Translation of simetría

At around seven, it wasn't dark anymore, the mother of the family offered me some tea. I felt so uncomfortable coming to a new family owned casa and vomiting there all night, but I was really sick.
The tour started soon and we first visited the ruins nearby, which was a ten minutes drive. A tour guide introduced us to each and every pyramid and told us stories about practically every stone.
I boarded the AA flight to Cancun, and got there around two o'clock. It was my first time in Mexico. On the same night I had a flight booked to Havana, but I did not know whether I should take it.