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Encyclopedia of Physical Science and Technology EN010H-470 July 16, 2001 16:53

310 Nanosized Inorganic Clusters

The central Mo positions of the 12 {(Mo)Mo 5 } pentagons 60 identical protein subunits coded only by one gene.
V 2+
define an icosahedron and the 30 [Mo 2 O 4 ] a truncated These form the 12 pentagonal capsomers (morphology
icosahedron. This corresponds to the formulation [{(Mo) units), each capsomer consists of five protomers.
V
Mo 5 O 21 (H 2 O) 6 } 12 {Mo 2 O 4 (CH 3 COO)} 30 ] 42− . The ball- Such spherical {Mo 132 }-type clusters have been re-
like structure (Fig. 10) is also documented in the cry- ferred to in the literature as Keplerates corresponding to
¯
stal structure (space group Fm3) with cubic Kepler’s model of the cosmos and his concept of plan-
closest-packed spheres in the salt (NH 4 ) 42 [Mo VI 72 etary motion, as described in his early opus Mysterium
V
Mo 60 O 372 (CH 3 COO) 30 (H 2 O) 72 ] • ca. 300 H 2 O • ca. 10 Cosmographicum. In accordance with this speculative
CH 3 COONH 4 . model, Kepler believed that the distances between the
This molecular system with its 60 MoO 6 subunits, cor- orbits of the planets could be explained if the ra-
responding to the 12 related {(Mo)Mo 5 } pentagons, rep- tios between the successive orbits were designed to
resents a topological model for spherical viruses, e.g., the be equivalent to the spheres successively circumscribed
most simple satellite tobacco necrosis virus (STNV) with around and inscribed within the five Platonic solids.

FIGURE 13 Polyhedral representation of the {Mo 57 M 6 } cluster with its basic building blocks and their constituents
along the C 3 (upper left) and along one of the three C 2 axes (upper right). On the upper right, one {Mo 17 } building

block consisting of one {Mo } and two {Mo 8 } groups, and on the upper left, one {Mo 8 } unit is shown by dark gray
1
shading. Also shown by dark gray shading are one {Mo } group (built up from two face-sharing octahedra) and one

2
MO 6 unit ( cross hatched). For comparison, the polyhedral representations of the {Mo 36 } cluster structure, consisting
∗
of two {Mo 17 } building blocks linked by two {Mo } units, are shown in the related views, also highlighting one {Mo 8 }
1
(bottom left) and one {Mo 17 } building block (bottom right). It is important to recognize the relationship between the
{Mo 8 } and the pentagonal {(Mo)Mo 5 } groups (see text). ({Mo 8 }: light gray (central MoO 7 pentagonal bipyramid: white),

{Mo }: black, {Mo }: hatched, {Mo }: cross hatched)
∗

2 1 1