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No. Any Syncom satellite would be too big, even for A3 size paper. Well, it could be done but the model would need an internal structure that would end up being a huge project in and of itself.
The model is scale 1:1. It's an old sat, so it's not a modern cubesat, nor a life-size Hubble Space Telescope (Sorry for that. Maybe next year.....)
Here's another clue : a (light) sensor.
The next hint by Monday or Tuesday.
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Erik
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