Create Salesforce Case object with nested relationships using REST API

I am attempting to create a new Case object using the REST API but need to find out how to format the JSON body to pass in nested SObjects. It's not apparent in the Docs, and I can't seem to find any examples. Anyone have any pointers or have done this before? The SF web UI uses a text lookup field to set the (related) Contact and Account, and I need to figure out how to either bypass the need for a lookup or embed the SObjects of the related records in the JSON. ``` [{"message":"The value provided for foreign key reference Contact is not a nested SObject","errorCode":"INVALID_FIELD"}] ```