Seventy-five years ago, the May 1940 issue of Popular Science carried the plans for this novelty crystal set that was suitable for mailing as a letter. You could slip it into an envelope “and mail to one of your radio-minded friends as an amusing birthday or holiday greeting.”
The radio was sandwiched inside two postcards, with the detector and taps for the tuning coil exposed. Connections for antenna, ground, and headphones were made to paper fasteners which also held the “chassis” together.
To keep it flat, the coil was wound “spider web” style, with four taps for tuning. Blobs of solder were left exposed, and a “crocodile clip” was used to make the connections.
The whole radio could be mailed for six cents. The schematic is shown below:
All of the parts for this set should be easily obtainable. If you need help finding any (the most difficult to find would be the high-impedance earphone), I have sources on my crystal set parts page.