tldr; I realized I am more productive when not interrupted during tasks that require thinking (specifically, ignoring phone calls and emails while working).
I thought this was going to be about an actual 26 hour day, which is entirely possible (and a very interesting subject).. but don't even think about maintaining a 26 hour schedule in 24 hours of time.
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.
With a 28 hour day you'd come full circle in a week (I think), but with 6 days in your week instead of 7, and 120 hrs awake vs 112 hrs.
Edit: oops, just noticed jgeralnik beat me to it, with illustrations and all!
How long as he been maintaining this new schedule for? If he only started this a week ago, what's to say that this won't change the next week with an ever more optimised formula?