A cryovial storage system is provided for use in LNVP storage and transportation freezers. The system comprises a hexagonal box that can be used modularly in both vertical and horizontal dimensions to more efficiently fill the functional space within cryogenic freezers and dry shippers. Also provided is a canister and insert system configured to receive a stack of hexagonal boxes (or multiple stacks of hexagonal boxes) and a method for accessing only the topmost box in a stack while retaining the other boxes in the stack below and a system that provides ease of transferability of boxes between storage freezers and dry shippers.