The material structure described by Ti20(AlSi3)3 crystallizes in the monoclinic Pm space group. There are sixteen inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 8-coordinate geometry to two equivalent Ti(1), one Al(2), one Al(3), one Si(2), one Si(5), one Si(6), and one Si(8) atom. In the second Ti site, Ti(2) is bonded in a 8-coordinate geometry to two equivalent Ti(2), one Al(1), one Si(1), one Si(3), one Si(4), one Si(7), and one Si(9) atom. In the third Ti site, Ti(3) is bonded in a 8-coordinate geometry to two equivalent Ti(3), one Al(1), one Al(3), one Si(2), one Si(4), one Si(6), and one Si(8) atom. In the fourth Ti site, Ti(4) is bonded in a 8-coordinate geometry to two equivalent Ti(4), one Al(2), one Si(1), one Si(3), one Si(5), one Si(7), and one Si(9) atom. In the fifth Ti site, Ti(5) is bonded in a 5-coordinate geometry to one Al(2), one Si(1), one Si(2), and two equivalent Si(5) atoms. In the sixth Ti site, Ti(6) is bonded in a 5-coordinate geometry to one Al(1), one Al(3), one Si(3), and two equivalent Si(4) atoms. In the seventh Ti site, Ti(7) is bonded in a 5-coordinate geometry to one Al(2), one Al(3), one Si(2), and two equivalent Si(6) atoms. In the eighth Ti site, Ti(8) is bonded in a 5-coordinate geometry to one Al(1), one Si(1), one Si(3), and two equivalent Si(7) atoms. In the ninth Ti site, Ti(9) is bonded in a 5-coordinate geometry to one Al(1), one Al(3), one Si(2), and two equivalent Si(8) atoms. In the tenth Ti site, Ti(10) is bonded in a 5-coordinate geometry to one Al(2), one Si(1), one Si(3), and two equivalent Si(9) atoms. In the eleventh Ti site, Ti(11) is bonded in a 5-coordinate geometry to two equivalent Al(2), one Si(5), one Si(6), and one Si(9) atom. In the twelfth Ti site, Ti(12) is bonded in a 5-coordinate geometry to two equivalent Al(1), one Si(4), one Si(7), and one Si(8) atom. In the thirteenth Ti site, Ti(13) is bonded in a 5-coordinate geometry to two equivalent Al(3), one Si(4), one Si(6), and one Si(8) atom. In the fourteenth Ti site, Ti(14) is bonded in a 5-coordinate geometry to one Si(5), one Si(7), one Si(9), and two equivalent Si(1) atoms. In the fifteenth Ti site, Ti(15) is bonded in a 5-coordinate geometry to one Si(5), one Si(6), one Si(8), and two equivalent Si(2) atoms. In the sixteenth Ti site, Ti(16) is bonded in a 5-coordinate geometry to one Si(4), one Si(7), one Si(9), and two equivalent Si(3) atoms. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a 9-coordinate geometry to one Ti(6), one Ti(8), one Ti(9), two equivalent Ti(12), two equivalent Ti(2), and two equivalent Ti(3) atoms. In the second Al site, Al(2) is bonded in a 9-coordinate geometry to one Ti(10), one Ti(5), one Ti(7), two equivalent Ti(1), two equivalent Ti(11), and two equivalent Ti(4) atoms. In the third Al site, Al(3) is bonded in a 9-coordinate geometry to one Ti(6), one Ti(7), one Ti(9), two equivalent Ti(1), two equivalent Ti(13), and two equivalent Ti(3) atoms. There are nine inequivalent Si sites. In the first Si site, Si(1) is bonded in a 9-coordinate geometry to one Ti(10), one Ti(5), one Ti(8), two equivalent Ti(14), two equivalent Ti(2), and two equivalent Ti(4) atoms. In the second Si site, Si(2) is bonded in a 9-coordinate geometry to one Ti(5), one Ti(7), one Ti(9), two equivalent Ti(1), two equivalent Ti(15), and two equivalent Ti(3) atoms. In the third Si site, Si(3) is bonded in a 9-coordinate geometry to one Ti(10), one Ti(6), one Ti(8), two equivalent Ti(16), two equivalent Ti(2), and two equivalent Ti(4) atoms. In the fourth Si site, Si(4) is bonded in a 9-coordinate geometry to one Ti(12), one Ti(13), one Ti(16), two equivalent Ti(2), two equivalent Ti(3), and two equivalent Ti(6) atoms. In the fifth Si site, Si(5) is bonded in a 9-coordinate geometry to one Ti(11), one Ti(14), one Ti(15), two equivalent Ti(1), two equivalent Ti(4), and two equivalent Ti(5) atoms. In the sixth Si site, Si(6) is bonded in a 9-coordinate geometry to one Ti(11), one Ti(13), one Ti(15), two equivalent Ti(1), two equivalent Ti(3), and two equivalent Ti(7) atoms. In the seventh Si site, Si(7) is bonded in a 9-coordinate geometry to one Ti(12), one Ti(14), one Ti(16), two equivalent Ti(2), two equivalent Ti(4), and two equivalent Ti(8) atoms. In the eighth Si site, Si(8) is bonded in a 9-coordinate geometry to one Ti(12), one Ti(13), one Ti(15), two equivalent Ti(1), two equivalent Ti(3), and two equivalent Ti(9) atoms. In the ninth Si site, Si(9) is bonded in a 9-coordinate geometry to one Ti(11), one Ti(14), one Ti(16), two equivalent Ti(10), two equivalent Ti(2), and two equivalent Ti(4) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ti20(AlSi3)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.170
_cell_length_b   7.552
_cell_length_c   13.051
_cell_angle_alpha   89.952
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   509.544
_cell_formula_units_Z   1
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
  Ti  Ti0  1  0.754  0.006  0.667  1.0
  Ti  Ti1  1  0.752  0.503  0.170  1.0
  Ti  Ti2  1  0.754  0.496  0.830  1.0
  Ti  Ti3  1  0.752  0.003  0.330  1.0
  Ti  Ti4  1  0.246  0.496  0.830  1.0
  Ti  Ti5  1  0.248  0.003  0.330  1.0
  Ti  Ti6  1  0.246  0.006  0.667  1.0
  Ti  Ti7  1  0.248  0.503  0.170  1.0
  Ti  Ti8  1  0.500  0.256  0.500  1.0
  Ti  Ti9  1  0.500  0.757  0.003  1.0
  Ti  Ti10  1  0.500  0.616  0.622  1.0
  Ti  Ti11  1  0.500  0.120  0.127  1.0
  Ti  Ti12  1  0.500  0.124  0.875  1.0
  Ti  Ti13  1  0.500  0.620  0.374  1.0
  Ti  Ti14  1  0.000  0.745  0.500  1.0
  Ti  Ti15  1  0.000  0.245  0.000  1.0
  Ti  Ti16  1  0.000  0.877  0.878  1.0
  Ti  Ti17  1  0.000  0.375  0.374  1.0
  Ti  Ti18  1  0.000  0.375  0.625  1.0
  Ti  Ti19  1  0.000  0.875  0.126  1.0
  Al  Al20  1  0.500  0.394  0.001  1.0
  Al  Al21  1  0.500  0.892  0.499  1.0
  Al  Al22  1  0.500  0.801  0.802  1.0
  Si  Si23  1  0.500  0.303  0.304  1.0
  Si  Si24  1  0.500  0.303  0.695  1.0
  Si  Si25  1  0.500  0.804  0.198  1.0
  Si  Si26  1  0.000  0.607  1.000  1.0
  Si  Si27  1  0.000  0.107  0.499  1.0
  Si  Si28  1  0.000  0.700  0.697  1.0
  Si  Si29  1  0.000  0.197  0.195  1.0
  Si  Si30  1  0.000  0.194  0.806  1.0
  Si  Si31  1  0.000  0.698  0.305  1.0
[/CIF]
.
The material structure described by Ti20(AlSi3)3 crystallizes in the monoclinic Pm space group. There are sixteen inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 8-coordinate geometry to two equivalent Ti(1), one Al(2), one Al(3), one Si(2), one Si(5), one Si(6), and one Si(8) atom. In the second Ti site, Ti(2) is bonded in a 8-coordinate geometry to two equivalent Ti(2), one Al(1), one Si(1), one Si(3), one Si(4), one Si(7), and one Si(9) atom. In the third Ti site, Ti(3) is bonded in a 8-coordinate geometry to two equivalent Ti(3), one Al(1), one Al(3), one Si(2), one Si(4), one Si(6), and one Si(8) atom. In the fourth Ti site, Ti(4) is bonded in a 8-coordinate geometry to two equivalent Ti(4), one Al(2), one Si(1), one Si(3), one Si(5), one Si(7), and one Si(9) atom. In the fifth Ti site, Ti(5) is bonded in a 5-coordinate geometry to one Al(2), one Si(1), one Si(2), and two equivalent Si(5) atoms. In the sixth Ti site, Ti(6) is bonded in a 5-coordinate geometry to one Al(1), one Al(3), one Si(3), and two equivalent Si(4) atoms. In the seventh Ti site, Ti(7) is bonded in a 5-coordinate geometry to one Al(2), one Al(3), one Si(2), and two equivalent Si(6) atoms. In the eighth Ti site, Ti(8) is bonded in a 5-coordinate geometry to one Al(1), one Si(1), one Si(3), and two equivalent Si(7) atoms. In the ninth Ti site, Ti(9) is bonded in a 5-coordinate geometry to one Al(1), one Al(3), one Si(2), and two equivalent Si(8) atoms. In the tenth Ti site, Ti(10) is bonded in a 5-coordinate geometry to one Al(2), one Si(1), one Si(3), and two equivalent Si(9) atoms. In the eleventh Ti site, Ti(11) is bonded in a 5-coordinate geometry to two equivalent Al(2), one Si(5), one Si(6), and one Si(9) atom. In the twelfth Ti site, Ti(12) is bonded in a 5-coordinate geometry to two equivalent Al(1), one Si(4), one Si(7), and one Si(8) atom. In the thirteenth Ti site, Ti(13) is bonded in a 5-coordinate geometry to two equivalent Al(3), one Si(4), one Si(6), and one Si(8) atom. In the fourteenth Ti site, Ti(14) is bonded in a 5-coordinate geometry to one Si(5), one Si(7), one Si(9), and two equivalent Si(1) atoms. In the fifteenth Ti site, Ti(15) is bonded in a 5-coordinate geometry to one Si(5), one Si(6), one Si(8), and two equivalent Si(2) atoms. In the sixteenth Ti site, Ti(16) is bonded in a 5-coordinate geometry to one Si(4), one Si(7), one Si(9), and two equivalent Si(3) atoms. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a 9-coordinate geometry to one Ti(6), one Ti(8), one Ti(9), two equivalent Ti(12), two equivalent Ti(2), and two equivalent Ti(3) atoms. In the second Al site, Al(2) is bonded in a 9-coordinate geometry to one Ti(10), one Ti(5), one Ti(7), two equivalent Ti(1), two equivalent Ti(11), and two equivalent Ti(4) atoms. In the third Al site, Al(3) is bonded in a 9-coordinate geometry to one Ti(6), one Ti(7), one Ti(9), two equivalent Ti(1), two equivalent Ti(13), and two equivalent Ti(3) atoms. There are nine inequivalent Si sites. In the first Si site, Si(1) is bonded in a 9-coordinate geometry to one Ti(10), one Ti(5), one Ti(8), two equivalent Ti(14), two equivalent Ti(2), and two equivalent Ti(4) atoms. In the second Si site, Si(2) is bonded in a 9-coordinate geometry to one Ti(5), one Ti(7), one Ti(9), two equivalent Ti(1), two equivalent Ti(15), and two equivalent Ti(3) atoms. In the third Si site, Si(3) is bonded in a 9-coordinate geometry to one Ti(10), one Ti(6), one Ti(8), two equivalent Ti(16), two equivalent Ti(2), and two equivalent Ti(4) atoms. In the fourth Si site, Si(4) is bonded in a 9-coordinate geometry to one Ti(12), one Ti(13), one Ti(16), two equivalent Ti(2), two equivalent Ti(3), and two equivalent Ti(6) atoms. In the fifth Si site, Si(5) is bonded in a 9-coordinate geometry to one Ti(11), one Ti(14), one Ti(15), two equivalent Ti(1), two equivalent Ti(4), and two equivalent Ti(5) atoms. In the sixth Si site, Si(6) is bonded in a 9-coordinate geometry to one Ti(11), one Ti(13), one Ti(15), two equivalent Ti(1), two equivalent Ti(3), and two equivalent Ti(7) atoms. In the seventh Si site, Si(7) is bonded in a 9-coordinate geometry to one Ti(12), one Ti(14), one Ti(16), two equivalent Ti(2), two equivalent Ti(4), and two equivalent Ti(8) atoms. In the eighth Si site, Si(8) is bonded in a 9-coordinate geometry to one Ti(12), one Ti(13), one Ti(15), two equivalent Ti(1), two equivalent Ti(3), and two equivalent Ti(9) atoms. In the ninth Si site, Si(9) is bonded in a 9-coordinate geometry to one Ti(11), one Ti(14), one Ti(16), two equivalent Ti(10), two equivalent Ti(2), and two equivalent Ti(4) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ti20(AlSi3)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.170
_cell_length_b   7.552
_cell_length_c   13.051
_cell_angle_alpha   89.952
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   509.544
_cell_formula_units_Z   1
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
  Ti  Ti0  1  0.754  0.006  0.667  1.0
  Ti  Ti1  1  0.752  0.503  0.170  1.0
  Ti  Ti2  1  0.754  0.496  0.830  1.0
  Ti  Ti3  1  0.752  0.003  0.330  1.0
  Ti  Ti4  1  0.246  0.496  0.830  1.0
  Ti  Ti5  1  0.248  0.003  0.330  1.0
  Ti  Ti6  1  0.246  0.006  0.667  1.0
  Ti  Ti7  1  0.248  0.503  0.170  1.0
  Ti  Ti8  1  0.500  0.256  0.500  1.0
  Ti  Ti9  1  0.500  0.757  0.003  1.0
  Ti  Ti10  1  0.500  0.616  0.622  1.0
  Ti  Ti11  1  0.500  0.120  0.127  1.0
  Ti  Ti12  1  0.500  0.124  0.875  1.0
  Ti  Ti13  1  0.500  0.620  0.374  1.0
  Ti  Ti14  1  0.000  0.745  0.500  1.0
  Ti  Ti15  1  0.000  0.245  0.000  1.0
  Ti  Ti16  1  0.000  0.877  0.878  1.0
  Ti  Ti17  1  0.000  0.375  0.374  1.0
  Ti  Ti18  1  0.000  0.375  0.625  1.0
  Ti  Ti19  1  0.000  0.875  0.126  1.0
  Al  Al20  1  0.500  0.394  0.001  1.0
  Al  Al21  1  0.500  0.892  0.499  1.0
  Al  Al22  1  0.500  0.801  0.802  1.0
  Si  Si23  1  0.500  0.303  0.304  1.0
  Si  Si24  1  0.500  0.303  0.695  1.0
  Si  Si25  1  0.500  0.804  0.198  1.0
  Si  Si26  1  0.000  0.607  1.000  1.0
  Si  Si27  1  0.000  0.107  0.499  1.0
  Si  Si28  1  0.000  0.700  0.697  1.0
  Si  Si29  1  0.000  0.197  0.195  1.0
  Si  Si30  1  0.000  0.194  0.806  1.0
  Si  Si31  1  0.000  0.698  0.305  1.0
[/CIF]
.