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it's a regular nonagon also known as enneagon ....
 i hope it helps....
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Let the number of sides be n and use the formula: 1/2n(n-3) = diagonals

1/2n(n-3) = 27

Multiply both sides by 2 and then form a quadratic equation:

n2-3n-54 = 0

Solving the above quadratic equation works out as:

n = -6 or n = 9 it must be the latter because the sides can't be negative

Therefore the polygon has 9 sides.
its called regular nanogon where nano means 9.
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