Some friends of mine believe that “search” has been solved. They explain that they can almost always find what they are looking for, and quickly, using keyword search. My life is much more frustrating! There are all sorts of things I look for and can’t find. An additional source of frustration is that I don’t know when to give up, when to conclude that what I’m looking for isn’t there.

Recently I had this experience with a question I thought would make a good blog challenge:

Does there exist a polyhedron such that all of its faces are nonconvex?

If you can think up a proof or example, please post your answer in the comments section, but with “Spoiler alert:” at its start. If you find an answer through a web search, give us the URL and tell us your search strategy. A URL pointing to discussion of this exact question would also be acceptable, even if the discussion doesn’t provide an answer.

I’d like to give a prize, and thought about various prizes (a Tcho chocolate bar? treating the winner to coffee? …) but decided in true blog spirit to ask for suggestions for an appropriate prize.

P.S. I thought about defining  terms such as “polyhedron” and “nonconvex” here.  But since this is a search and/or geometry challenge, any readers who do not know the meaning of these 3D geometry terms can still participate. I would be particularly delighted if someone who did not understand the question initially was able to find a solution.

Update: An answer has been found. Congratulations, Francine. However I realize I mixed up two searches, and this one isn’t as hard as I thought I remembered.