Marvel’s Avengers is filled with different resources you will need to collect. Many of them can be found by playing through missions and smashing up the resource boxes that are hidden throughout the game. One resource you won’t be able to collect this way is Polychoron. Polychoron is quite important and is used to upgrade your Avenger’s major artifact. If you want to truly unlock you Avenger’s full potential, you will need a lot of Polychoron to do it.
Thankfully, you can get some as a reward for beating by completing Faction Assignments. Not all of these challenges will reward you with Polychoron, so if you have limited time to play the game be sure you are completing challenges that will give you the rewards you need.
You won’t actually get access to faction assignments until a few hours into the game. You will first need to play through the missions that lead you up to finding Tony Stark, and bringing Iron Man back into the Avengers.
The Faction Assignments are not particularly difficult and tend to revolve around completing fairly simple actions like kills certain types of enemies, looting certain types of resources, and playing missions in a certain way. For example, you may need to kill aerial units or take out enemies with a certain type of attack to keep SHIELD happy and get your hands on the resource.