Construct a pentagon/stars
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The five-pointed star is merely a pentagram with the enclosed area filled in and the lines erased. This is such a common symbol that there is little point listing its uses; it's seen on everything from the flags of US and China to bottles of beer.
The solid star, three-dimensional in appearance, is the most challenging contruction we will present -- but only a step from the others. Mastery of this figure is quite gratifying and qualifies the intermediate geometer.