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A 'concave decagon' is a ten-sided shape with every other corner pushed in towards the centre. It forms a regular five-pointed star.
yes
A geometric star shape is concave. A star that is in the sky is convex.
The correct term for a "star shape" would be a pentagram, for 5 pointed ones, hexagram for 6, and etc etc. I suppose it was nicknamed the "star" because of its points that streak out similar to a star.