This is the pop out basket I initially displayed at #mrrf18. The basket can lay flat and appear as a trivet or you can lift up and rotate the handle where it pops out into a 5 section basket.
Print the test model to see if the pop up mechanism works well, if too stiff lower your flow rate and if too loose increase your flow rate. Print the top part on a raft to avoid the cuts getting fused together. The top get glued to the base, be sure to only glue the pegs and the area close to the peg so that the basket can still pop up.