We report, for the first time, the formation of the icosahedral phase (i-phase) in rapidly quenched Ti73-xV27Sixalloys, where 13 ≤ × ≤ 25. Transmission electron microscopy (TEM) lattice image studies show that the i-phase occurs with b.c.c. phase of large unit cell. Diffraction studies demonstrate that the two phases are coherently related; the cubic ⟨001⟩ directions are parallel to three of the two-fold icosahedral axes, the ⟨111⟩ directions are parallel to the threefold icosahedral axes and the ⟨530⟩ cubic directions are nearly parallel to the fivefold directions. The b.c.c. lattice constant, a0= 12·98 Å, is related to he quasilattice constant, 4·72 Å, suggesting different projections from the same six-dimensional cubic lattice. These observations demonstrate the similarity of these two structures. A determination of the atom locations in this crystalline phase should provide information of the atomic positions in the icosahedral phase.