In the Mn-Si alloy system, there is the intermetallic-compound ν phase around Mn-18at.%Si. Its crystal structure called the ν structure has been reported to involve complex coordination polyhedra with coordination numbers (CN's) 12, 14, and others. To clarify whether one of these polyhedra can be identified as a structural unit or not in the ν structure, we have investigated the crystallographic features of the (R → R + ν) reaction in Mn-15at.%Si alloy samples by transmission electron microscopy. In Mn-15at.%Si samples obtained by cooling from the single R phase at a relatively fast cooling rate, metastable precipitates were found to be present in the R-structure matrix. Their notable feature is that each precipitate involves regions exhibiting characteristic electron diffraction patterns, which indicate the presence of metastable states, in addition to the initial amorphous and final ν states. Based on the careful analysis of these patterns, it was understood that the metastable states were directly associated with the formation of the ν structure, and that the formation started with the appearance of dodecagonal atomic columns. Because a dodecagonal column is characterized by a one-dimensional array of CN14 polyhedra, among the coordination polyhedra involved in the ν structure, a CN14 polyhedron can be identified as its structural unit.