This is a spherical version of Viktor Genel's "ReCube" coordinate motion puzzle. I think this is one of his best designs and he has given me permission to reproduce it here.
Viktor has a website and for more information about ReCube, see his blog posts:
http://viktorg.com/wordpress1/2012/06/17/13-recube/
http://viktorg.com/wordpress1/2011/09/26/10-tricube-or-forward-to-past/
The puzzle consists of three identical pieces that slide together simultaneously to form a sphere, similarly to the Venn Puzzle. It's not super hard but I think it looks terrific in red, green, and blue as pictured here. My Shapeways shop (https://www.shapeways.com/product/YLK6Y7767/recube-sphere) and my i.materialise shop (https://i.materialise.com/en/shop/item/recube-sphere) have these pieces available in white and a variety of other colors (and at a lower price). You can save some money by buying the buying pieces in white and dyeing them yourself with fabric dye (e.g., Rit DyeMore).
Unless you request otherwise, I will ship the puzzle assembled and include a flattened cubical plastic box that fits it exactly.
Product code: ReCube buying Sphere