Cue up the Beatles' I'll follow the sun and admire this rotating tiny house that does exactly that.
A hundred years ago, George Bernard Shaw did his best work in his rotating writing shed. There are some big advantages; he could turn it toward the sun when it was cool, away from it when it is hot. Lester Walker notes that "it could be manually turned to follow the arc of the sun. He worked alone and loved his privacy; he even adjusted his telephone for outgoing calls only." (More on Shaw's hut here)
Now, Portland Oregon's Path Architecture has built 359, a bigger shed that does much the same thing; it is 12 feet by 12 feet and has it all. Compared to the 8'-6" of your standard tiny house, it is really roomy inside.
There is an off-grid design with composting toilet and solar on the roof, shown on the model;
This built version is tied to city services with a flush toilet, the waste going through a rotating coupling used in the natural gas industry that is in the dead center of the turntable. Electricity and water connections are the reason it only turns 359 degrees, so that they don't get all twisted up, but Benjamin Kaiser tells TreeHugger that "for the next version, however, we have that licked too."
There really are lots of advantages to a rotating tiny house; Just as Shaw found, you can follow the sun all day (although it looks like those kids really have to work to make it happen) avoid the sun on the hottest days and capture it on the coldest. And it looks like a lot of fun.