Mackay polyhedron

Mackay polyhedra becomes reduced to the representative tiles of the coexisting tilings with either acute and obtuse rhombohedra (tT ) or the inscribed tetrahedra G and F tT ), as in Figures 12-6 and 12-7. 

Boudard model. Not only have we shown that the atomic decorations in a shape of Bergman and Mackay polyhedra can not be stable clusters but also we have drawn the appearance of the cut polyhedra on the surfaces that matches the image of the real material on the fivefold surface. 

The polyhedron corresponding to the Neovius surface has the same arrangement of points as that for the infinite semi-regular polyhedral surface 6.43 discussed above, but the spaces between the points are differently filled with polygons so that each of the 48 points per cubic cell has the configuration of 8.4.8.6 and this leads to a surface of genus of 9. This surface has two kinds of flat points and is thus not regular (Mackay Terrones 1991). 12 tubes in the [110] directions connect cavities. 

Figure 12-3. left) A Bergman (B) and right) a Mackay (Me) polyhedron as an atomic decoration of the icosahedral tiling in the model M T ( ) (see Ref. ). The standard length along the twofold... 

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