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Construction: Pentagram and Stars

It's not hard to construct a pentagram instead of a pentagon. Just stop short after Step 5; instead of drawing lines connecting A, B, C, D, E and back to A, draw lines AC, CE, EB, BD, and DA.

Fill the pentagram to make a star; this will look best if the pentagram is first drawn lightly with a hard pencil and then nearly erased.

The solid star is related to the *decagon*. Given a decagon, draw all the diagonals; these are all diameters of the circumscribing circle. Wise choices of what to erase and what to fill in make the solid star.

On the other hand, given an inscribed star or pentagram, the decagon can be constructed by extending lines through existing vertices and intersections until they meet the circumscribing circle.

Can you construct a *stellated decagon*? Is there more than one kind?