Archimedean antiprism

Structural characteristics of compounds with X Me = 8 are collected in Table 17. Na3NbF8 and Na3TaF8 compounds that form similar crystal structure [77], The structure of Na3TaF8 was determined by Hoard et al. [136], by means of X-ray diffraction of a single crystal. Na3TaF8 is composed of sodium cations and isolated complex ions TaF83, in an Archimedean antiprism configuration, as shown in Fig. 23. 

The intensely yellow compounds 10 and 11 crystallize in the tetragonal space group PA/nnc. The oval Ei0Lii6 cluster skeleton (E = P, As) is topologically best described as a twofold capped Archimedean antiprism formed by the 10 E atoms, of which each of the 16 triangular faces are occupied by a lithium center (Fig. 12) (21). 

Fig. 12. (Left) Molecular structure of the mixed-valent cluster 10 and 11 in the crystal. (Right) Representation of the E10-dicapped-Archimedean antiprism as anionic partial structure in 10 and 11 (E = P, As). For clarity the organic groups of the silyl groups have been omitted.

If we have N hard spheres (of radius rs) forming a close-packed polyhedron, another sphere (of smaller radius rc) can fit neatly into the central hole of the polyhedron if the radius ratio has a well-defined value (see also 3.8.1.1). The ideal radius ratio (rc/rs) for a perfect fit is 0.225.. (in a regular tetrahedron, CN 4), 0.414.. (regular octahedron CN 6), 0.528.. (Archimedean trigonal prism CN 6), 0.645... (Archimedean square antiprism CN 8), 0.732.. (cube CN 8), 0.902... (regular icosahedron CN 12), 1 (cuboctahedron and twinned cuboctahedron CN 12). 

Fig. 33. Skeletons of the gold clusters (Au(AuL)8] and [Au(AuL)io] compared with the icosahedron and the bicapped Archimedean antiprism. Central atoms are shaded peripheral atoms are unshaded.

The anion can be described as a slightly distorted Archimedean antiprism with Xe—F distances ranging from 1.946 to 2.099 A. The eight-fold xenon coordination provides no clearly defined position for the lone pair, thus seemingly being in violation of the VSEPR theory. 

Three or more molecules may assemble in the solid state to form a finite assembly with connecting forces propagated in 3D. The components of such an assembly will typically form a polyhedral shell. The shell may accommodate chemical species as guests. The polyhedron may be based on a prism or antiprism, as well as one of the five Platonic (e.g. cube, tetrahedron) or 13 Archimedean (e.g. truncated tetrahedron) solids.4... 

The Archimedean semi-regular solids, prisms, and antiprisms... 

For BgClg the triangular dodecahedron is calculated to be the most stable as long as C = 1.77 but when C = 0 the bicapped trigonal antiprism is more stable. Since natural BgClg is dodecahedral, we have here more evidence that C should be positive. The dodecahedron can be considered a distortion of the square (Archimedean) antiprism. ... 

The B resonance spectra of both the C,C 1,6-dimethyl- and C,C 1,10-dimethyl-carbadecaboranes have been examined at 19-3 Mc./sec., and the results have again been reported twice the conclusions drawn on each occasion were the same, viz., the structure was that of a bicapped Archimedean antiprism with carbon atoms at... 

The XYg-type molecule may take the form of (I) a cube (O/,), (II) an archimedean antiprism (D4J), (III) a dodecahedron (D2j), or (IV) a face-centered trigonal prism (C21 ). Although XYg molecules are rare. X-ray analysis indicates that [TaFg] and [CrOg] ions take structures II and III, respectively [1339,1340]. The infrared and Raman spectra of crystalline Na3[TaFg] are in accord with structure II, proposed by X-ray analysis [1341]. However, the vibrational spectra of the [IFg] and [TeFg] ions support the archimedean antiprism structures [1332] shown below ... 

For normal coordinate analyses of a cubic and an Archimedean antiprism XYg molecule, see Refs. 1342 and 1343, respectively. 

Incidentally, the regular prisms and the regular antiprisms are also semiregular, i.e., Archimedean, solids. Moreover, the second prism, in its most symmetrical configuration, is a regular solid, the cube and the first antiprism, in its most symmetrical configuration, is also a regular solid, the octahedron. 

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