We have found a series of new rare earth boron-rich solids in REBC(N) (RE: Y, Ho, Er, Tm, and Lu), systems and their structures are solved from single crystal and/or powder X-ray diffraction data. Structure analysis results show that they are homologous with B(4)C and also show trigonal symmetry. As the two basic structural units, boron icosahedra and octahedra in the new phases form in layers and stack in different sequences which form different phases. With increasing number of icosahedral layers stacking between two neighboring octahedral layers, the c-axis of the unit cell is increased and the other two edges of the unit cell are only changed slightly. Three monophases of the series have been synthesized both in powders and as single crystals. The vibrational modes of the homologous phases are analyzed from the Raman spectra and compared with that of B(4)C.