We present an atomistic molecular dynamics investigation of the structural time evolution of isolated polyphenylene dendrimers, carbon based dendrimers with a planar core formed by a 1,3,5 trisubstituted benzene ring. Simulations are carried out at low (80 K) and room temperature. A general classification of the conformations (core conformations) assumed by the three dendrimer branches with respect to the planar core is presented. It is found that out of the six possible core conformations only four are stable, the remaining two being unstable for steric reasons. For second generation dendrimers, two of the four accessible core conformations are associated with an open arrangement of the three branches attached to the planar 3-fold core of the dendrimer, whereas the remaining two are associated with a collapsed arrangement of two branches. At low temperature the initial conformation is generally conserved whereas at room temperature jumps among the four possible core conformations are observed in the nanosecond time range. For second generation dendrimers the core conformation jumps are associated with an oscillation between two global shape states: open and collapsed. The computed bistability of the global shape suggests additional possible functional uses for some of these carbon based dendrimers.