Antiprism, Archimedean square

If we have N hard spheres (of radius rs) forming a close-packed polyhedron, another sphere (of smaller radius rc) can fit neatly into the central hole of the polyhedron if the radius ratio has a well-defined value (see also 3.8.1.1). The ideal radius ratio (rc/rs) for a perfect fit is 0.225.. (in a regular tetrahedron, CN 4), 0.414.. (regular octahedron CN 6), 0.528.. (Archimedean trigonal prism CN 6), 0.645... (Archimedean square antiprism CN 8), 0.732.. (cube CN 8), 0.902... (regular icosahedron CN 12), 1 (cuboctahedron and twinned cuboctahedron CN 12). 

For BgClg the triangular dodecahedron is calculated to be the most stable as long as C = 1.77 but when C = 0 the bicapped trigonal antiprism is more stable. Since natural BgClg is dodecahedral, we have here more evidence that C should be positive. The dodecahedron can be considered a distortion of the square (Archimedean) antiprism. ... 

Square Archimedean antiprism Tricapped trigonal prism, D y ... 

Rh,P(CO)2,] - p Capped Archimedean antiprism, the fragment RhgP has square antiprism structure 36... 

Crystalline fluorocarbonates, Ba2R(C03)2F3 (R = Y, Gd), of interest fortheir potential application in optics, were synthesized hydrothermally from RFj and BaC03 in molten Ba(N03)2 at 700°C and 216 MPa pressure (Mercier and Leblanc 1991). In these fluorocarbonates the Ba and R cations occupy the center of distorted BaOgF4 and ROgp3 Archimedean antiprisms monocapped on a square face. Two Ba-containing polyhedra are connected by an R-containing polyhedron to yield Ba2ROi2p9 blocks which are then connected to form infinite two-dimensional slabs. 

---