Since both the Td and Oh point groups belong to cubic symmetry, if we consider any structure in which the center of mass of both the structure coincide together, then what will be symmetry for the composite structure?
If I understand you correctly, and both phases have the same orientation (unit cells are identically aligned) than the composite has the lower symmetry, i.e., -43m (Td) and not m-3m (Oh).
If the alignment of the basis vectors are different, the final symmetry will be even lower. Finally only this symmetry will remain which exists in both groups. I don't see any point how a "center of mass" influence this. Could you explain, what do you mean with this term regarding point group symmetry?
If I understand you correctly, and both phases have the same orientation (unit cells are identically aligned) than the composite has the lower symmetry, i.e., -43m (Td) and not m-3m (Oh).
If the alignment of the basis vectors are different, the final symmetry will be even lower. Finally only this symmetry will remain which exists in both groups. I don't see any point how a "center of mass" influence this. Could you explain, what do you mean with this term regarding point group symmetry?
IN addition to Gerd Noltze's answer, to solve your answer, consider the Wyckoff positions for the two space groups, see http://www.cryst.ehu.es/ Many of the Wyckoff positions in space group Pm-3m will split into two positions in the lower symmetry group. Additionally, if you have different lattices you will end up with a primitive lattice.
Let me add this further info. If you "merge" two groups that have an identical lattice (at least as far as the base vectors are concerned, the centering is flexible) you will end up with one of the common subgroups. See the Bilbao Server subgroup relationships or look at the International tables for crystallography for common subgroups of m-3m and -43m.
Thank you for your answers and happy new year. Regarding the attribution for the center of mass of two separate entities, kindly follow the figure attached. I want to find the symmetry of the structure formed by superimposing point A on the point B, together they retain their position at point C.
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