In Mathematica and Wolfram Language, with the feature called Texture it's easy to draw 3D solids such as polyhedra with image textures on the surface such as the faces of polyhedra. When playing with this, I drew a rhombic hexecontahedron (properties), the logo of Wolfram|Alpha with national flags on its faces:

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☝ Rhombic hexecontahedron wrapped with the 60 most populous countries' national flags, one different flag drawn on each of the 60 rhombic faces. (It's somewhat odd that the most populous countries happen to have a lot of red and green colors in their national flags.)

The code is in my Git repository.

Remarks:

• It was a bit tricky to understand what the option VertexTextureCoordinates is and does, and how to set it up for what I'm trying to draw. It turns out for putting the national flags on the faces of a rhombic hexecontahedron, since both are (usually) isomorphic to a square, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}} is would work as it aligns the four vertices of a rectangular flag to the four vertices of a rhombic face.

Something left to be improved:

• Avoid flags that's not isomorphic to the face of the given polyhedron;

• Compute the suitable values of VertexTextureCoordinates to reduce or even avoid distortion of the flags;

• Find a reasonable way to align national flags of shapes not isomorphic to the shape of a face of a given polyhedron, such that the main feature of the national flag wrapped on a polyhedron face is well recognizable.