Summary
The Recovery Mode installer of Catalina appears to not be able to properly partition the drive. Install High Sierra or earlier macOS from Recovery Mode and then upgrade to Catalina or install Catalina (or High Sierra) from a bootable drive.
The Details
After upgrading to Catalina (from the Catalina beta) I kept having Internet dropouts after my iMac would sleep for a period of time. The only way to get Internet back was to reboot. Shutdown also was taking a long time so I decided to backup my computer (always backup your computer!) and do a clean install of Catalina to determine if the problem was with the Catalina upgrade, software on my system, or perhaps a physical issue.
I started getting this error after trying to to do a clean install of Catalina on my iMac. I entered the Recovery mode, erased the primary drive, and tried to do an install of Catalina. It would run for an hour or more and then I would get this error. I thought this may be related to my connectivity issues so I tried using different wireless networks and dragging an ethernet cable through my house to the router but with no success.
I believe repartitioning the drive was the mistake. Catalina uses a split drive setup where all of the system files are on an inaccessible system partition and the user files are on a separate partition. I believe that by creating a single partition drive the Catalina installer was unable to properly partition the disk and would stall until the Internet connection was finally dropped and the installation failed.
I've now restored to the macOS that came with my iMac, High Sierra, through Recovery mode. I will now do an upgrade to Catalina through the normal methods.
If you can't access a previous version of macOS through Recovery you can create a bootable USB drive that will install macOS High Sierra. Go to https://support.apple.com/en-us/HT201372 for those details. It looks like you can make a bootable Catalina drive but since I am trying to determine if Catalina is the cause of my issue I am going back to High Sierra for a little bit.