Given that 𝜷-Bi4I4 is the first weak topological insulator (TI) (identified by us, but not shown here), that 𝜶-Bi4I4 is a prototype higher-order TI (highlighted here), and that there is a room-temperature transition between the two structural phases (also identified by us, but not shown here), we have established a new (quasi-1D) TI paradigm that unifies the first and second order topological insulators. The topological nature of 𝜶-Bi4I4 was not predicted by topological quantum chemistry (or symmetry indicators) that has exhaustively analyzed all the available materials in the materials database. Thus, our results imply the possible existence of many topological materials beyond the scope of our current knowledge and accelerate the discovery of a new generation of functional materials in the topological age.