We report here the formation of a class of materials in the rapidly so
lidified Ti68Fe26Ni1Si5 system based on transmission electron microsco
pic exploration of the electropolished melt-spun ribbons. The phase re
ported here pertains to a modification of the icosahedral phase leadin
g to tetrahedral symmetry with no discernible periodicities, unlike th
ose of earlier known rational approximant phases. The analysis of the
selected area diffraction patterns of these phases revealed variable l
inear phason strains in the shifted spots of undistorted twofold recip
rocal rows. The experimentally observed reciprocal vectors in these di
rections have been suggested to arise owing to their dependence on bot
h the physical and pseudospace components vis-re-vis that of the icosa
hedral phase. It has been argued that such a dependence may arise owin
g to the presence of the nonlinear motif having components in both the
spaces in the higher-dimensional structural description.