Is there a way to create a file folder using the REST API or a Trigger?

[ForeGolfer]

I'm using the REST API to create a new record (Case).  The Case will then need to create a new folder with the Case ID as the folder name to store files that I will import.  I haven't been able to create a folder using the REST API or a Trigger and I'm wondering if anyone knows how to do that?

I don't see an endpoint for the creating the folder in the swagger documentation.

[CoopperBackpack]

Hello @ForeGolfer,

The methods listed in Swagger UI are the available methods.

So, as for the object creation, it is only possible to create a Table. All the other objects should be created manually in the account. 
As for the Triggers, they only work with the existing tables and fields of these Tables.