A prism whose ends are 18-gons.
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It has 20 faces. The number of edges will depend on the exact configuration of the shape. For example, a icosahedron in the form of a prism, with 18-gons as bases, will have 54 edges. On the other hand a pyramid with a 19-gon base will have 38 edges. A bipyramid with a decagon base will have 30 edges. There are very many more possible shapes.
By definition, an icosahedron has 20 faces. The number of edges can be 30 (Platonic solid), 38 (19-gonal pyramid), 54 (18-gonal prism). Other, topologically different icosahedra also exist but are difficult to describe in just words.
20% of 54 = 54 x (1 - (20/100)) = 54 x 0.8 = 43.2
6/20 = 54/B so B = 54*20/6 = 180
Total number of faces = 9*6 = 54 Number of "hidden" faces = 2*(9 - 1) = 16 So number of painted faces = 54 - 16 = 38