Graphite and diamond are both made from carbon atoms, but the atoms are arranged in different ways. Consequently, they have different physical properties (diamond hardness=10, graphite= less than 1). Other examples of structures that are polymorphs of one another are the silica minerals (quartz is an example). You can see how different structures are built from the same basic pieces by viewing these movies:
Note that the above movies all depict minerals with composition = SiO2.