Polyhedra ellipsoid

Fig. 7. Structure of the singly-bridged Au-oxo complex, 3. Top left, combination polyhedral/ball-and-stick representation right, thermal ellipsoid plot. The PO4 and WOe polyhedra (or W atom) are shown in lighter and darker gray. Bottom left. X-ray structure of the coordination polyhedron...

Figure 2.28 An ORTEP view of the crystal structure of Eu(L )3(TPTZ) with partial atomic labeling. Thermal ellipsoids are drawn at the 50% probability level [25]. (Reprinted from Polyhedron, 26, C.R. De Silvaa, J.R. Maeyera, A. Dawsona and Z. Zheng, Adducts of lanthanide [l-diketonates with 2,4,6-tri(2-pyridyl)-l,3,5-triazine synthesis, structural characterization, and photoluminescence studies, 1229-1238, 2007, with permission from Elsevier.)...

Since equation 10.8 is true for any polyhedron, it will also be true for any tessellation of both the sphere and the ellipsoid. Thus both of these must have genus g-0. In contrast, the genus for a tessellation of the torus will be g l which can be seen from Figure 10.5. 

Figure 3.3.2 The TaTy polyhedron and surrounding K ions. Displacement ellipsoids (spheres for the isotropic F atoms) are drawn at the 50% probability level. (Symmetry code (i) x, 1/2-v z ) 0-K TaF...

The Shape of a Polyhedron as Defined by its Moments of Inertia and Momental Ellipsoid... 

The shape of a coordination polyhedron can be defined by its moments of inertia and the shape of the corresponding momental ellipsoid (Figure 4). Thus, consider a rigidly oriented collection of n particles such as a set of n ligands located at the vertices of a coordination polyhedron. The moment of inertia of this collection of particles about any axis passing through its center of mass is defined as... 

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