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I bought one of these from Decathon, Southampton.
http://www.decathlon.co.uk/vioo-100-rear-led-bike-light-black-id_8322808.htmlttp://www.decathlon.co.uk/vioo-100-rear-led-bike-light-black-id_8322808.html
Held on by a rubber band. Seems quite a clever minimalistic idea.
Is it an old idea? Is there a generic term for the design?
It's a few years old at least, lots of companies do similar. I believe Knog may have been the first, or at least had the largest marketing budget of the early adopters.
I've got a cheap Lidl of a similar design, just a bit of elastic to hold it on.
Upside is it looks so cheap you can leave it on the bike and not worry about it being nicked, downside is it tends to point down due to the angle of the seatpost.