Pentagonal antiprism

The symmetry axis with maximum strength for each function of set I is 69° 1.35 from the fivefold axis of the pentagonal antiprism, corresponding to the ratio 0.38341 of half height to radius of the antiprism, with the corresponding values for set II of 41° 47.65 and 1.1186. 

Removal of two vertices from a deltahedron leads to arachno polyhedra having 2n + 6 skeletal electrons according to the Wade-Mingos rules [13-16]. Among the many theoretical possibilities for arachno polyhedra, the pentagonal antiprism, generated by removal of a pair of antipodal vertices from an icosahedron, is the most significant in bare post-transition metal cluster chemistry. 

The third DFT study [96] was motivated by the existence of the stable pentagonal antiprismatic cluster [93] Pd Biio" found in Bii4PdBri6. This cluster is an example of a cluster with an interstitial atom that obeys the Wade-Mingos rules [13-16]. Thus, the pentagonal antiprism is derived from an icosahedron by removal... 

However, a quantum-chemical analysis indicates the stability of the ZnsSnsBig cluster core. It can be described as a Zn-centered monocapped pentagonal antiprism, which is equivalent to an icosahedron with one missing apex atom, and consists of a planar Zns unit which is coplanar with an (Sn/Bi)s five-membered ring. As in [Zn ... 

Pd Bi o]" + is an example of an arachno cluster in the compound [Pd Bi, ) (BiBr j ). It has 2n + 6 skeleton electrons if one assumes one lone electron pair per Bi atom and a neutral Pd atom. The Bi atoms form a pentagonal antiprism which is the same as an icosahedron with two missing vertices. 

The repulsion energy calculations show that the most stable structure is formed by replacing two adjacent atoms at the vertices of an icosahedron by a single atom at the midpoint of that edge. This edge coalesced icosahedron is slightly more stable than the closely related capped pentagonal antiprism formed by removal of one of the vertices formed by an icosahedron ... 

Several Ln(II) coronates and cryptates have been isolated, but few crystal structures are known. One example is given in Fig. 4.22 in which Eu(II) is sandwiched between two B15C5 coronands. The metal ion lies on an inversion centre and is ten coordinate with an environment close to a pentagonal antiprism, with approximate Dsa geometry. From the Eu-O distances, an ionic radius of about 1.39 A can be calculated, as compared to the standard value of 1.33 A, which means that the Eu-O bond lengths are somewhat longer than usual. 

A polynuclear anion [Nig(CO),2] reacts with a deficit of GeCl4 in acetonitrile to form [GeNi,2(CO)22] xs tetrachloride yields [GeNi,o(CO)2o] - These compounds represent the first examples of encapsulated Ge, which is contained in a pentagonal antiprism in the Ni species, and this is bicapped in the Ni,2 species. 

It consists of a pentagonal antiprism of nickel atoms encapsulating a germanium atom. Each nickel atom possesses one terminal and one edgebridging (along the pentagons) carbonyl. 

It can be viewed as a Ni10Bi2 icosahedron encapsulating a Ni atom, as well as a Ni,0 pentagonal antiprism, with an eleventh Ni atom placed in its cavity, capped, on opposite sides, by two Bi atoms. 

The mineral johachidolite has been identified as CaAlB307, in which the Ca is ten-co-ordinate (distorted pentagonal antiprism), the Al is six-co-ordinate (octahedral), and the B is four-co-ordinate (tetrahedral). The structure is built up by the periodic tessellation of triangles, squares, and hexagons, forming an AIB3O7 lattice, with the Ca + ions situated at the centres of hexagons. 

Pig. 3.3 Single metal nodes and selected SBUs used in the construction of MOFs a tetrahedral metal ion b octahedral metal ion c [M2(COO)4] paddle-wheel SBU d [MOICOO) ] trimer SBU e [M40(C00)e] quad-core SBU f [M4Cl(COO)8] quad-core SBU g [M4Cl(trz)8] quad-core SBU and h [Feio02o(COO)io] pentagonal antiprism SBU... 

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