17. Paper ball from triangles and squares // The snub cube // paper model

📌 This polyhedron can be inscribed in a regular cube in such a way that its six square faces will be coplanar with those of the cube but will be in a slightly twisted position. Each square is entirely surrounded by triangles accounting for twenty four of these. Then eight more triangles close the remaining spaces to complete the solid.

This suggests the following colour arrangement. The squares may have three colours in opposite pairs. Each of these square faces will be entirely surrounded by triangles of the same colour. Thus the same three colours will occur in the triangles but shifted to maintain the map colouring principle. Finally the other eight triangles share a fourth colour.