Truncated cubes

From a geometrical point of view only, this structure could be compared with that of CsCl, with 1 Ca in place of Cs, and the centre of a 6 B octahedron in place of the Cl atom (in the centre of the cell with its axes parallel to the cell axes). Ca is surrounded by 24 B in a regular truncated cube (octahedra and truncated cubes fill space). A number of hexaborides (of Ca, Sr, Ba, Y and several lanthanides and Th, Np, Pu, Am) have been described as pertaining to this structural type. 

Fig. 9.9 The 13 Archimedean solids, in order of increasing number of vertices. Truncated tetrahedron (1), Cuboctahedron (2), Truncated cube (3), Truncated octahedron (4), Rhombicubocta-hedron (5), Snub cube (6), Icosidodecahedron (7),...

Snub Prisms is also called Diirer octahedron (see it on the painting Melencolia I by Dtirer, 1514, depicting the muse of mathematics at work) and it can be obtained by truncating Cube on two opposite vertices. 

Figure 4.21. Pictures of self-assembled crystals with open structure, (a, b) An array of truncated octahedra, with simple cubic symmetry, (c, d) An array of truncated cubes, with fee symmetry, (e, f) An array of truncated tetrahedra. (g, h) An array of truncated cubes, with bcc symmetry, (i, j) An array of truncated cubes. Each cube in (i, j) has solder on only four of its eight triangular faces. (Reprinted with permission from Science, 1999, 284, 948-951. Copyright 1999 American Association for the...

Fig. 16.7 HRTEM micrographs and reconstructed shapes of anatase Ti02 nanoparticles (a, b) truncated cube (c, d) prism [Copyright Wiley-VCH Verlag GmbH Co. KGaA. Reproduced with permission from Feldhoff et al, (2007)]...

Figure 11.36 By extending the polyol reaction for a ven time period, various polyhedral shapes capped with 100 and 111 faces can be obtained in high yield, a) A schematic of the nucleation and growth process, in which silver continuously deposits onto the 100 faces to eventually result in a completely 111 -bound octahedron, b to f) SEM images of cubes, truncated cubes, cuboctahedra, truncated octahedra, and octahedra, respectively (scale bar 100 nm). Reproduced with permission from reference [91]. (2006) Wiley-VCH Verlag GmbH Co. KGaA.

Wiley, B., Herricks, T., Sun, Y. and Xia, Y. (2004). Polyol synthesis of silver nanoparticles Use of chloride and oxygen to promote the formation of singlecrystal, truncated cubes and tetrahedrons. Nano Lett. 4 1733-1739. 

Figure 2.4 shows the 13 Archimedean polyhedra with their names, which indicate some of the family relationships. Each of the polyhedra is conventionally regarded as derived by a process of truncation on vertices or edges from a Platonic parent — thus the truncated cube has 8 triangular faces formed by cutting off the vertices of the cube, the truncated octahedron has 6 square faces, derived by cutting off vertices of an octahedral parent, and so on. 

Figure 2.11 The results of pairwise contractions of the vertices of the hexagons of the regular orhit cage of 0[, symmetry, again with the colour coding as in Figure 2.7. The first pairing choice, column 1, leads to the 24-vertex cage of the truncated cube, while the second choice leads to a further copy of the small rhombicuboctahedron.

Define notations, b, c, and d for a truncated cube, g and s for truncated octahedron, as shown in Figure 5.20, and t for a growth time, then v(lll), v(lOO), and the a-parameter are expressed as shown in Table 5.1. This method has a great advantage that no comparison of diamond crystal shapes in an interval of growth time t is... 

Figure 5.20. A truncated cube before (I) and after (II) a removal of the corners, and one of the prisms removed (ill). A cubic crystal (IV) with two triangular prisms removed which impinge on one another. A cubic crystal (V) with all the triangular prisms removed, and one of the hexagonal faces produced (VI) [87].

Truncated tetrahedron (TT) Truncated cube(TC) Truncated octahedron(TO)... 

Figure 27.16 Tetrahedral class of the cubic system, (a) Truncated cube, (b) Tetrahedron developed from the cube.

Figure 8.2 I Truncated cube model of aluminium foam, and folds that develop in the cruciform section on compressive yield (adapted from Santosa S. and Wierzbicki T. J. Mech. Phys. Solids, 46, 645, 1998).

---