The instantaneous elastodynamic Poynting vector and its time-averaged complex cognate can be used to visualize not only the instantaneous energy flux associated with elastodynamic waves but also their traveling and standing wave components. A novel geometric interpretation is made for the instantaneous Poynting vector in an elastodynamic medium to aid in that visualization. It is noted that the geometry of the instantaneous Poynting vector's time evolution can, with suitable symmetries in the geometry of the medium, and thus of the stress tensor, be related to the time-averaged complex Poynting vector.