"I thought this was going to be about an actual 26 hour day, which is entirely possible (and a very interesting subject).."
Do you mean sleeping 'x' amount of time every '26-x' hours? That is a very interesting notion. It creates an illusion of having more hours in a day. Of course, this comes at cost. If you were to sleep at 12.00am one day, you will have to sleep at 2am the next, and 4am the day after that and so on.