The compound described by Cr3AlO6 is beta indium sulfide-derived structured and crystallizes in the trigonal P-3m1 space group. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1) and four equivalent O(4) atoms to form CrO6 octahedra that share corners with four equivalent Al(2)O4 tetrahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), two equivalent O(5), and two equivalent O(6) atoms to form CrO6 octahedra that share  a cornercorner with one Al(2)O4 tetrahedra, corners with three equivalent Al(1)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(4)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. In the third Cr site, Cr(3) is bonded to three equivalent O(4) and three equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Al(2)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. In the fourth Cr site, Cr(4) is bonded to six equivalent O(5) atoms to form CrO6 octahedra that share corners with six equivalent Al(1)O4 tetrahedra and edges with six equivalent Cr(2)O6 octahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2) and three equivalent O(5) atoms to form AlO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-58°. In the second Al site, Al(2) is bonded to one O(3) and three equivalent O(4) atoms to form AlO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-57°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Cr(1) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to three equivalent Cr(2) and one Al(1) atom. In the third O site, O(3) is bonded in a distorted trigonal pyramidal geometry to three equivalent Cr(2) and one Al(2) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Cr(3), two equivalent Cr(1), and one Al(2) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Cr(4), two equivalent Cr(2), and one Al(1) atom. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Cr(3) and two equivalent Cr(2) atoms. is represented by the CIF file [CIF]
data_AlCr3O6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.908
_cell_length_b   5.908
_cell_length_c   14.482
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   437.839
_cell_formula_units_Z   4
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Al  Al0  1  0.333  0.667  0.455  1.0
  Al  Al1  1  0.000  0.000  0.127  1.0
  Al  Al2  1  0.000  0.000  0.873  1.0
  Al  Al3  1  0.667  0.333  0.545  1.0
  Cr  Cr4  1  0.500  0.500  0.000  1.0
  Cr  Cr5  1  0.170  0.830  0.668  1.0
  Cr  Cr6  1  0.830  0.170  0.332  1.0
  Cr  Cr7  1  0.500  0.000  0.000  1.0
  Cr  Cr8  1  0.170  0.340  0.668  1.0
  Cr  Cr9  1  0.830  0.660  0.332  1.0
  Cr  Cr10  1  0.333  0.667  0.829  1.0
  Cr  Cr11  1  0.000  0.000  0.500  1.0
  Cr  Cr12  1  0.667  0.333  0.171  1.0
  Cr  Cr13  1  0.000  0.500  0.000  1.0
  Cr  Cr14  1  0.660  0.830  0.668  1.0
  Cr  Cr15  1  0.340  0.170  0.332  1.0
  O  O16  1  0.667  0.333  0.937  1.0
  O  O17  1  0.333  0.667  0.581  1.0
  O  O18  1  0.000  0.000  0.255  1.0
  O  O19  1  0.663  0.832  0.916  1.0
  O  O20  1  0.324  0.162  0.582  1.0
  O  O21  1  0.963  0.481  0.258  1.0
  O  O22  1  0.168  0.832  0.916  1.0
  O  O23  1  0.838  0.162  0.582  1.0
  O  O24  1  0.519  0.481  0.258  1.0
  O  O25  1  0.168  0.337  0.916  1.0
  O  O26  1  0.838  0.676  0.582  1.0
  O  O27  1  0.519  0.037  0.258  1.0
  O  O28  1  0.037  0.519  0.742  1.0
  O  O29  1  0.676  0.838  0.418  1.0
  O  O30  1  0.337  0.168  0.084  1.0
  O  O31  1  0.000  0.000  0.745  1.0
  O  O32  1  0.667  0.333  0.419  1.0
  O  O33  1  0.333  0.667  0.063  1.0
  O  O34  1  0.481  0.519  0.742  1.0
  O  O35  1  0.162  0.838  0.418  1.0
  O  O36  1  0.832  0.168  0.084  1.0
  O  O37  1  0.481  0.963  0.742  1.0
  O  O38  1  0.162  0.324  0.418  1.0
  O  O39  1  0.832  0.663  0.084  1.0
[/CIF]
.
The compound described by Cr3AlO6 is beta indium sulfide-derived structured and crystallizes in the trigonal P-3m1 space group. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1) and four equivalent O(4) atoms to form CrO6 octahedra that share corners with four equivalent Al(2)O4 tetrahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), two equivalent O(5), and two equivalent O(6) atoms to form CrO6 octahedra that share  a cornercorner with one Al(2)O4 tetrahedra, corners with three equivalent Al(1)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(4)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. In the third Cr site, Cr(3) is bonded to three equivalent O(4) and three equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Al(2)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. In the fourth Cr site, Cr(4) is bonded to six equivalent O(5) atoms to form CrO6 octahedra that share corners with six equivalent Al(1)O4 tetrahedra and edges with six equivalent Cr(2)O6 octahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2) and three equivalent O(5) atoms to form AlO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-58°. In the second Al site, Al(2) is bonded to one O(3) and three equivalent O(4) atoms to form AlO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-57°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Cr(1) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to three equivalent Cr(2) and one Al(1) atom. In the third O site, O(3) is bonded in a distorted trigonal pyramidal geometry to three equivalent Cr(2) and one Al(2) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Cr(3), two equivalent Cr(1), and one Al(2) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Cr(4), two equivalent Cr(2), and one Al(1) atom. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Cr(3) and two equivalent Cr(2) atoms. is represented by the CIF file [CIF]
data_AlCr3O6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.908
_cell_length_b   5.908
_cell_length_c   14.482
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   437.839
_cell_formula_units_Z   4
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Al  Al0  1  0.333  0.667  0.455  1.0
  Al  Al1  1  0.000  0.000  0.127  1.0
  Al  Al2  1  0.000  0.000  0.873  1.0
  Al  Al3  1  0.667  0.333  0.545  1.0
  Cr  Cr4  1  0.500  0.500  0.000  1.0
  Cr  Cr5  1  0.170  0.830  0.668  1.0
  Cr  Cr6  1  0.830  0.170  0.332  1.0
  Cr  Cr7  1  0.500  0.000  0.000  1.0
  Cr  Cr8  1  0.170  0.340  0.668  1.0
  Cr  Cr9  1  0.830  0.660  0.332  1.0
  Cr  Cr10  1  0.333  0.667  0.829  1.0
  Cr  Cr11  1  0.000  0.000  0.500  1.0
  Cr  Cr12  1  0.667  0.333  0.171  1.0
  Cr  Cr13  1  0.000  0.500  0.000  1.0
  Cr  Cr14  1  0.660  0.830  0.668  1.0
  Cr  Cr15  1  0.340  0.170  0.332  1.0
  O  O16  1  0.667  0.333  0.937  1.0
  O  O17  1  0.333  0.667  0.581  1.0
  O  O18  1  0.000  0.000  0.255  1.0
  O  O19  1  0.663  0.832  0.916  1.0
  O  O20  1  0.324  0.162  0.582  1.0
  O  O21  1  0.963  0.481  0.258  1.0
  O  O22  1  0.168  0.832  0.916  1.0
  O  O23  1  0.838  0.162  0.582  1.0
  O  O24  1  0.519  0.481  0.258  1.0
  O  O25  1  0.168  0.337  0.916  1.0
  O  O26  1  0.838  0.676  0.582  1.0
  O  O27  1  0.519  0.037  0.258  1.0
  O  O28  1  0.037  0.519  0.742  1.0
  O  O29  1  0.676  0.838  0.418  1.0
  O  O30  1  0.337  0.168  0.084  1.0
  O  O31  1  0.000  0.000  0.745  1.0
  O  O32  1  0.667  0.333  0.419  1.0
  O  O33  1  0.333  0.667  0.063  1.0
  O  O34  1  0.481  0.519  0.742  1.0
  O  O35  1  0.162  0.838  0.418  1.0
  O  O36  1  0.832  0.168  0.084  1.0
  O  O37  1  0.481  0.963  0.742  1.0
  O  O38  1  0.162  0.324  0.418  1.0
  O  O39  1  0.832  0.663  0.084  1.0
[/CIF]
.