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(-1)

it should be 5 but the game says 10

(+2)

It has ten corners. 5 are the points, 5 are between the points. 

(-1)

a pentagon has 5 corners. a full pentagon is a star.

(+2)

A pentagon has five corners. I didn't get a pentagon in the game; I got a pentagram which has 10 corners.

actually, because of how lines work, a pentagram has 5 corners.

Actually, because the shape has not only five corners, but five vertices of the inner pentagon as well, a pentagram has 10 corners.  It is like five triangles placed around a 5-cornered pentagon. A pentagram keeps the 5 corners from the pentagon and adds each of the points of each triangle which are also corners, albeit much smaller ones than in the pentagon.