How can I find the smaller symmetric structure from big crystal unit cell? I have Pyrope (Mg3Al2(SiO4)3) crystal structure, downloaded from materialsproject: 
https://materialsproject.org/materials/mp-6073/#

It appeared as triclinic cell, but if you download CIF file and open it from softwares like Avogadro or VESTA, it appeared as a orthogonal simple cubic (a=b=c, alpha = beta = gamma = 90 degree). I also checked that this geometry is the same with what I downloaded from American Mineralogy Material Database. 

Now, I wish to run DFT or quantum calculations for them. So, I excluded atoms in periodic boundary, unit cell contains total 160 atoms. I'm afraid this might be too big, might takes too long time to calculate via DFT or any other quantum simulations. All I need to do is just geometry optimizations, but still, 160 atoms seems too big. 

Using VESTA or Avogadro or any other software, is this possible to find the symmetric structure inside this or other "big" unit cell, and make a smaller / simpler version of unit cell for faster calculation? 

Or, can I manually cut this unit cell in 1/4 size, 40 atom system with 1/2 size for x, y, and z direction, and run the minimization? It seems that the Pyrope unit cell have some sort of repeating structure inside the big unit cell. But I'm not sure if it is "safe" to find symmetry and divide the unit cell manually. 

Thank you
The structure contains 4 independent atoms, Mg, Al, Si and O. The space group is a cubic one containing 96 asymmetric units. If you place an atom on a general position, it will appear 96 times in the unit cell. Mg, Al, and Si are located in various special positions, i.e. lie on symmetry elements. Placing the Mg and the Si atom will result in 24 atoms in unit cell, while placing the Al atom in its position (on the origin) will result in 16 atoms in the unit cell (on a three-fold and on the center of inversion).

So you could say that the asymmetric unit contains one oxygen atom, one quarter Mg and Si atom respectively (24/96), and one sixth Al atom (16/96). One of the sites you cited in a previous question gives the fractional coordinates as:

Si: 0.3750 0.0000 0.2500

Al: Origin

Mg: 0.1250 0.0000 0.2500

O: 0.0341 0.0490 0.6530

If you look at the space group, http://img.chem.ucl.ac.uk/sgp/large/230az1.gif,



you can see that Al, Mg, and Si are on special positions (you can either find the locations on the diagram or apply the 96 operations (48 combined with the I-centering) listed on the right to the coordinates and see how many unique locations you get), while oxygen is not.


  can I manually cut this unit cell in 1/4 size, 40 atom system with 1/2 size for x, y, and z direction, and run the minimization?


If you software is aware of crystallographic symmetry, it is a very simple system with 4 degrees of freedom (the oxygen position and the lattice parameter a). Everything else is fixed if you impose the symmetry of garnet.


  I have Pyrope (Mg3Al2(SiO4)3) crystal structure, downloaded from materialsproject: https://materialsproject.org/materials/mp-6073/#. It appeared as triclinic cell...


There are some inconsistencies in the way the site shows the data. The space group is (correctly) given as Ia3d. The 3D image does not show a body-centered cubic cell, but instead the primitive rhombohedral cell (the smallest unit that recreates the entire crystal through three translations). In one iteration ("primitive"), the coordinate file lists the symmetry as 1, applied the Ia3d operators to the atomic positions (maybe to "not to confuse" users unaware of crystal symmetry), and switched to the rhombohedral cell.