I store our home use eggs in this skelter which I found online - I can't remember where. It has a minor problem in that you have to be careful removing eggs as they sometimes roll down too quickly and crack... not hard to control the roll.
I also have eggs that I sell, and those are kept in cardboard flats. If I put 2 side by side then each row is 1 dozen. I load left to right and front to back. I don't refrigerate those and they are washed just before sale. Once they are washed and boxed, they are kept refrigerated.
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