A polyhedron with 13 or more faces.
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Dodecahedron
When you say "sides", do you mean faces or edges? A dodecahedron has 12 faces and 30 edges.
A 20-sided shape is called a dodecahedron.
A rhombic dodecahedron is a 3-D shape (polyhedron) that has 12 rhombic faces, 24 edges (sides), and 14 vertices (points). Its dual is a cuboctahedron. If you wanted to try by yourself, get a transparent model and start counting!
Dodecagon. A pentagon has five sides, a polygon with 12 sides is a dodecagon. A dodecahedron has 12 regular facets.