This looks like a common "Six Piece Burr", but is actually a three piece cube puzzle designed by Jim Gooch. I have added a hole so it may be put on a chain (not included). The puzzle should not come apart when it is on the chain. The assembled puzzle is about the size of a walnut.
The fit on these ranges from perfect to tight, depending on printing variations. I buy them in polished white and then sand slightly for a perfect fit before dyeing them myself. If you buy the colored ones, you can still sand to adjust the fit although the sanding will remove the color. If you do this correctly, it will not show when the puzzle is assembled. The purple model pictured here was dyed by Shapeways and fit perfectly out of the box. You may need to ream out the holes because powdered nylon tends to stick in there. If you want a copy with a perfect fit and reamed holes see my etsy store.