Terrarium is a 1985 science fiction novel by American writer and essayist Scott Russell Sanders, published by Tor.
Inside these cities, (called the "Enclosure") taboos extend so far as to make uncovered legs and unpainted faces a horrific sin.
Due to likely ongoing large scale social engineering there are 12 stages for mating but most women have their reproductive organs removed or are used as breeders starting at the age of 13.
The book focuses on a man named Phoenix and a Wildergoer called Teeg Passio, daughter of a renowned deconstructor of the original Earth cities whose pieces and materials were used to create the Enclosure.
The book details how they and a group of others escape out into the wilds and find an outside world they didn't expect.