Conjoined twins are rare - with less than a dozen adult pairs living in the world today.
Lori and Reba share 30% of their brain
Only a few hundred pairs of conjoined twins are born across the globe each year - appearing about once in every 100,000 births.
They face a dilemma - whether to opt for a life-threatening operation to separate them or to stay together.
Conjoined twin sisters Lori and Reba Schappell have chosen the latter and against all odds, lead independent and fulfilling lives.
The American twins' unusual lifestyle is documented in the BBC Radio 4 programme "Still Joined".
The programme makers say that on seeing the twins you are "immediately conscious of their physical difference" and "feel sorry for them".
This is not a reaction they appreciate.
The twins, aged 42, are joined at the head, but still manage to lead independent lives.
They share 30% of their brain tissue and their non functional left eye.
Reba has spina bifida and is unable to walk.
They face in opposite directions and have never seen each other's faces without the aid of a mirror.
Although their brains are joined, they insist they have separate thoughts, emotions and personalities.
The twins, from Pennsylvania, enjoy being together and cannot contemplate living separately. They do not want to live apart.
They said: "We're happy as we are.
"Why should we risk our lives just to conform to what society wants.
"If we're separated the chances are one or both of us will die.
"Even if the operation is successful, we won't suddenly become normal, we'll be severely physically disabled. "
The twins hate being labelled.
Lori said: "My name is not 'Conjoined Twin Schappell!'
"My name is Lori Lynn Schappell. I am a human being. Like, I'm a person. I am a PERSON.
"I have a soul. I have a heart. I'm one body.
The twins each pursue their own interests
"I have my legs, my arms. I am not this thing called a conjoined twin. I am attached to another person because an egg, the eggs did not separate, the two eggs did not separate.
They are fiercely independent.
They said: "We don't need any group to help us with anything because we have no problems.
"There is nothing that we can't handle ourselves, and that we have to go find out from another set of conjoined twins: 'What should I do here? And what should I do there?'
"Because it's different with every conjoined set of twins. You know, it's not like people with cancer.
"People who have breast cancer they all really have the same kind of breast cancer. Breast cancer is breast cancer."
Reba is a country singer who won the LA music award for Best New Country Artists in 1997, she has performed across the USA and in Germany and Japan.
Lori works part-time in a hospital laundry, taking positions that allow her to take time off for her sister's concert dates.
Reba said: "I live my life as I, as it comes. Because if you would dwell on it doesn't mean it's going to change it.
"You make your life. And if there's something that doesn't go right you fix it or you try to fix it.
"I like my life as I see it now. It's great! I'm healthy, that's what's the most important. I believe in "You make your own hell, or you make your own heaven."
Lori is the sister who makes the decisions.
She said: "I've always been the bossiest. She just does everything I say, you know, I'm like Mum, in this you know.
"She's like a kid, you know, Mothers tell their kids what to do, and they don't give up until the kid does whatever she's supposed to do, well you know, she's my kid so I tell her what to do."
Still Joined was broadcast on BBC Radio 4 at 1100 BST on Monday 3 May.