Simple methods are proposed to elucidate the basic symmetry components in order to understand the structure of polyhedral cage clusters. Such methods reduce the three-dimensional structure to two-dimensional pictures and allow the easier visualization and counting of vertices, edges and polygonal faces. Illustrations are given using examples of C 60, C 70, C 50 and C 28 clusters, atomic aluminium and argon clusters and pentagonal dodecahedron water clusters.