Tribromotris(4-methylpyridine)Mo(III), Acta Cryst. (1980) B36, 698. Two-circle optical goniometer measurements Faces Goniometer readings Distances N h k l Vc Ro d 1 0 1 1 6.85 42.42 1.10 2 0 -1 -1 186.85 137.58 1.10 3 0 1 -1 353.15 137.58 1.10 4 0 -1 1 173.15 42.42 1.10 5 -1 3 -1 324.04 106.56 1.80 6 -1 -2 -1 227.42 110.45 1.80 7 2 1 -1 75.94 104.99 2.20 8 -1 0 4 270.00 19.66 1.40 Morphological parameters from optical data a/b = .48934 alpha = 90.000 b/b = 1 beta = 96.220 c/b = .90724 gamma = 90.000 p0 = 1.85402 lambda= 90.000 q0 = .90190 mu = 83.780 r0 = 1 nu = 90.000 p0'= 1.86500 x0'= .10899 q0'= .90724 y0'= .00000 Coordinates of gnomonic projection poles h k l x' y' 0 1 1 .10899 .90724 0 -1 -1 - - 0 1 -1 - - 0 -1 1 .10899 -.90724 -1 3 -1 - - -1 -2 -1 - - 2 1 -1 - - -1 0 4 -.35726 .00000 Stereographic projection coordinates and interfacial angles Faces Observed Calculated angles with h k l Phi Ro Phi Ro (100) (010) (001) 0 1 1 6.85 42.42 6.85 42.42 85.39 47.95 42.05 0 -1 -1 186.85 137.58 186.85 137.58 94.61 132.05 137.95 0 1 -1 353.15 137.58 353.15 137.58 94.61 47.95 137.95 0 -1 1 173.15 42.42 173.15 42.42 85.39 132.05 42.05 -1 3 -1 324.04 106.56 324.05 106.56 124.25 39.12 110.14 -1 -2 -1 227.42 110.45 227.41 110.45 133.62 129.34 114.97 2 1 -1 75.94 104.99 75.93 105.00 20.44 76.43 98.95 -1 0 4 270.00 19.66 270.00 19.66 109.66 90.00 25.88 Morphological parameters from X-ray crystal data a/b = .48920( .00025) alpha = 90.000( .000) b/b = 1 beta = 96.260( .020) c/b = .90716( .00057) gamma = 90.000( .000) p0 = 1.85437( .00091) lambda= 90.000( .000) q0 = .90175( .00056) mu = 83.740( .020) r0 = 1 nu = 90.000( .000) p0'= 1.86550( .00092) x0'= .10969( .00035) q0'= .90716( .00057) y0'= .00000( .00000) Parameters & coordinates for gnomonic & stereographic projections Faces Gnomonic coordinates Stereographic coordinates h k l x' y' Phi Ro xs ys -1 -1 -1 - - 245.33 114.71 -3.028 -1.390 -1 -1 0 - - 244.07 90.00 -4.676 -2.274 -1 -1 1 -1.756 -.907 242.68 63.16 -2.840 -1.467 -1 0 -1 - - 270.00 116.85 -3.196 .000 -1 0 0 - - 270.00 90.00 -5.200 .000 -1 0 1 -1.756 .000 270.00 60.34 -3.023 .000 -1 1 -1 - - 294.67 114.71 -3.028 1.390 -1 1 0 - - 295.93 90.00 -4.676 2.274 -1 1 1 -1.756 .907 297.32 63.16 -2.840 1.467 0 -1 -1 - - 186.89 137.58 -.242 -2.003 0 -1 0 - - 180.00 90.00 .000 -5.200 0 -1 1 .110 -.907 173.11 42.42 .242 -2.003 0 0 -1 - - 270.00 173.74 -.284 .000 0 0 1 .110 .000 90.00 6.26 .284 .000 0 1 -1 - - 353.11 137.58 -.242 2.003 0 1 0 - - .00 90.00 .000 5.200 0 1 1 .110 .907 6.89 42.42 .242 2.003 1 -1 -1 - - 117.32 116.84 2.840 -1.467 1 -1 0 - - 115.93 90.00 4.676 -2.274 1 -1 1 1.975 -.907 114.67 65.29 3.028 -1.390 1 0 -1 - - 90.00 119.66 3.023 .000 1 0 0 - - 90.00 90.00 5.200 .000 1 0 1 1.975 .000 90.00 63.15 3.196 .000 1 1 -1 - - 62.68 116.84 2.840 1.467 1 1 0 - - 64.07 90.00 4.676 2.274 1 1 1 1.975 .907 65.33 65.29 3.028 1.390 Number of faces 26 Coordinates of the vertices (x,y,z are referred to a cartesian system of reference with the origin inside the crystal) N h1 k1 l1 h2 k2 l2 h3 k3 l3 x y z 1 0 1 1 0 1 -1 -1 3 -1 -.9886 1.6424 .1077 2 0 1 1 0 1 -1 2 1 -1 1.8800 1.6424 -.2049 3 0 1 1 0 -1 1 2 1 -1 2.6786 .0000 1.1981 4 0 1 1 0 -1 1 -1 0 4 .0073 .0000 1.4893 5 0 1 1 -1 3 -1 -1 0 4 -2.0884 1.0770 .7406 6 0 -1 -1 0 1 -1 -1 -2 -1 -1.9627 .0000 -1.2762 7 0 -1 -1 0 1 -1 2 1 -1 1.8800 .0000 -1.6950 8 0 -1 -1 0 -1 1 -1 -2 -1 -1.1640 -1.6424 .1269 9 0 -1 -1 0 -1 1 2 1 -1 2.6786 -1.6424 -.2919 10 0 1 -1 -1 3 -1 -1 -2 -1 -2.3367 .2564 -1.0028 11 0 -1 1 -1 -2 -1 -1 0 4 -2.0315 -1.0478 .7609 12 -1 3 -1 -1 -2 -1 -1 0 4 -3.0463 .2564 .3983 Coordinates of the vertices after rotation of the crystal by 18.43 degrees around z and by 9.47 degrees around y N xr yr zr 1 -.3889 1.8609 .2689 2 2.2466 .9825 -.5113 3 2.6935 -.8977 .7413 4 .2392 -.0797 1.4678 5 -1.4981 1.6346 1.0740 6 -2.0358 .6785 -.9360 7 1.4947 -.4982 -1.9811 8 -1.5888 -1.2017 .3166 9 1.9417 -2.3784 -.7285 10 -2.2621 1.0242 -.6048 11 -2.1136 -.4000 1.0847 12 -2.7074 1.1726 .8940 The Euler's criterion for convex polyhedra: 8 faces + 12 vertices = 18 edges + 2 is fulfilled Edges (a (+) means that the edge should be drawn by a solid line, a (-) by a dotted line) 1- 2 (+) 1- 5 (+) 1-10 (+) 2- 3 (+) 2- 7 (+) 3- 4 (+) 3- 9 (+) 4- 5 (+) 4-11 (-) 5-12 (-) 6- 7 (+) 6- 8 (-) 6-10 (+) 7- 9 (+) 8- 9 (-) 8-11 (-) 10-12 (-) 11-12 (-) Coordinates of the centres of the faces in the drawing N h k l yr zr 1 0 1 1 .700 .608 2 0 -1 -1 -.850 -.832 3 0 1 -1 .810 -.753 4 0 -1 1 -.992 .576 5 -1 3 -1 1.423 .408 6 -1 -2 -1 .255 .151 7 2 1 -1 -.698 -.620 8 -1 0 4 .582 1.130 View of the crystal after rotation by 18.43 degrees around z and by 9.47 degrees around y (orthogonal axes) +04 +11 +05 +12 +03 +08 +01 +02 +10 +09 +06 +07 Stereographic projection (radius = 10 cm) from optical goniometer data + *-1 0 4 + + + * 0-1 1 * 0 1 1 + Gnomonic projection from optical goniometer data *-1 0 4 O YR * 0-1 1 + * 0 1 1 XR Stereographic projection (radius = 10 cm) from X-ray data *-1 0 0 *-1-1 0 *-1 1 0 *-1 0 1 *-1-1 1 *-1 1 1 * 0-1 0 + * 0 1 0 * 0-1 1 * 0 0 1 * 0 1 1 * 1-1 1 * 1 1 1 * 1 0 1 * 1-1 0 * 1 1 0 * 1 0 0 Gnomonic projection from X-ray data .-1 0 0 .-1-1 0 .-1 1 0 + *-1-1 1 *-1 0 1 *-1 1 1 + O YR . 0-1 0 + * 0-1 1 * 0 0 1 * 0 1 1 + . 0 1 0 + * 1-1 1 * 1 0 1 * 1 1 1 + . 1-1 0 . 1 1 0 . 1 0 0 XR