Comment by JKCalhoun

Three pennies form an equilateral triangle with (of course) 60 degree angles.

Six of those equilateral triangles will perfectly add to 360 degrees. Intuitive enough? (I'm being a little hand-wavey by skipping over the part where each penny triangle shares two pennies with a neighbor — why the answer is not 18 for example.)

For my mind though, the intuitiveness ends in dimension 2 though. ;-)