text: ScBCSi (x = 0.030, y = 0.36 and z = 0.026) has a cubic crystal structure with space group F3m (No. 216) and lattice constant a = 2.03085(5) nm. This compound was initially identified as ScBC (phase I in the Sc-B-C phase diagram of figure 17). A small amount of Si was added into the floating zone crystal growth and thus this phase is a quaternary compound. Its rare cubic structure has 26 sites in the unit cell: three Sc sites, two Si sites, one C site and 20 B sites; 4 out of 20 B sites are boron-carbon mixed-occupancy sites. Atomic coordinates, site occupancies and isotropic displacement factors are listed in table VIII.
  In the unit cell, there are three independent icosahedra, I1, I2 and I3, and a B polyhedron which are formed by the B1–B4, B5–B8, B9–B13 and B14–B17 sites, respectively. The B polyhedron has not been observed previously and it is shown in figure 23. The icosahedron I2 has a boron-carbon mixed-occupancy site B,C6 whose occupancy is B/C=0.58/0.42. Remaining 3 boron-carbon mixed-occupancy sites are bridge sites; C and Si sites are also bridge sites.
  More than 1000 atoms are available in the unit cell, which is built up by large structure units such as two supertetrahedra T(1) and T(2) and one superoctahedron O(1). As shown in figure 24a, T(1) consists of 4 icosahedra I(1) which have no direct bonding but are bridged by four B and C20 atoms. These atoms also form tetrahedron centered by the Si2 sites. The supertetrahedron T(2) that consists of 4 icosahedra I(2) is the same as shown in figure 18b; its mixed-occupancy sites B and C6 directly bond with each other. The superoctahedron O(1) consists of 6 icosahedra I(3) and bridge sites B, C18, C1 and Si1; here Si1 and C1 exhibit a tetrahedral arrangement at the center of O(1). The B polyhedra also arrange octahedrally, without the central atom, as shown in figure 24c where the B and C19 atoms bridge the B polyhedra to form the octahedral supercluster of the B polyhedra.
  Using these large polyhedra, the crystal structure of ScBCSi can be described as shown in figure 25. Owing to the crystal symmetry, the tetrahedral coordination between these superstructure units is again a key factor. The supertetrahedron T(1) lies at the body center and at the edge center of the unit cell. The superoctahedra O(1) locate at the body center (0.25, 0.25, 0.25) of the quarter of the unit cell. They coordinate tetrahedrally around T(1) forming a giant tetrahedron. The supertetrahedra T(2) are located at the symmetry-related positions (0.25, 0.25, 0.75); they also form a giant tetrahedron surrounding T(1). Edges of both giant tetrahedra orthogonally cross each other at their centers; at those edge centers, each B polyhedron bridges all the super-structure clusters T(1), T(2) and O(1). The superoctahedron built of B polyhedra is located at each cubic face center.
  Scandium atoms reside in the voids of the boron framework. Four Sc1 atoms form a tetrahedral arrangement inside the B polyhedron-based superoctahedron. Sc2 atoms sit between the B polyhedron-based superoctahedron and the O(1) superoctahedron. Three Sc3 atoms form a triangle and are surrounded by three B polyhedra, a supertetrahedron T(1) and a superoctahedron O(1).