Yes, it can exist - assuming that was your question.
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In Geometry a 15 sided shape is called a pendedecagon polygon with 15 angles and sides
In Geometry a 15 sided shape is called a pendedecagon polygon with 15 angles and sides
A 15 sided shape is called a Pentadecagon, or a Pentakaidecagon.
The exterior angles of a 15 sided shape add up to 360 degrees
icosahedron