A 20-sided flat figure (polygon) is called an icosagon. If it is a solid figure--three-dimensional--it is an icosahedron.
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A regular twenty-sided polygon is called an icosagon.
Icosahedron is the shape, but it's just called 20 sided if you want to buy one.
A polygon with 20 sides is called either a 20-gon or an icosagon.
A shape, or polygon, with 24 sides is called an icosikaitera. Many people simply refer to it as a 24-gon.
a 4 sided shape is called a quadrilateral