Once you take the photos, you can process them through various pieces of software to produce a single image that can cover up to a full 360° - including the ceiling and floor underneath you.
I made my head primarily out of 20x20mm T-Slot aluminum that I purchased from Misumi. Instead of designing it all in advance and having Misumi ship me the precise correct length pieces, I have a couple meters of the material that I keep at home for various projects like this.
Fabrication of the head involved cutting the T-slot material to the right length, deburring / polishing the ends, cutting a few holes, and tapping screw threads into a piece of steel for attaching it to my tripod.
I made it in the metal shop at TechShop
Step 1: Understanding the Design
I ended up making the pieces a lot longer than I needed to. I will likely go back and shorten many of them.
You should also of course determine what hardware you need. Misumi has a very, very broad range of hardware. The prices vary enormously. There are some really nifty components that can add a lot to the cost.
For the nuts, I used spring-loaded post insertion nuts. This means that they don't slide around, and you can insert them in the middle of a rod - they are quite narrow. The standard nuts must be inserted at the end of a rod, so if you have something already assembled you may need to take it apart to insert a nut.
If you don't already know the distances needed for your camera's exit pupil alignment, you may want to make a longer version first and then chop off excess material.