We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have pmm, pmg, pgg or cmm symmetry [1]. These symmetry groups are members of the crystal class D2 among the 17 two-dimensional symmetry groups [2]. We display the algorithms’ output and give enumeration tables for small values...

The structure of cerium(IV) bis-(phosphite), Ce(HPO3)2, has been solved by single-crystal X-ray diffraction and has trigonal (P-3m1) symmetry. The cerium(IV) cation exhibits site symmetry -3m. and is octa-hedrally coordinated by O atoms of the phosphite ligands (point group symmetry 3m.). The highly symmetrical compound has a layered structure parallel to the ab plane, and is closely related to...

We theoretically and experimentally investigate the effect of imperfect vector symmetry on radially polarized beams focused by an aplanatic solid immersion lens at a numerical aperture of 3.3. We experimentally achieve circularly symmetric focused spot with a full-width-half-maximum of ~λ0/5.7 at λ0 = 1,310 nm, free-space wavelength. The tight spatial confinement and overall circular symmetry o...

The title compound, C(30)H(34)O(5), crystallizes with two symmetry-independent mol-ecules in the asymmetric unit. In the crystal structure, the two independent mol-ecules are disposed about a pseudo-center of inversion. An intra-molecular O-H⋯O hydrogen bond is observed in each independent mol-ecule. The crystal structure is stabilized by C-H⋯O hydrogen bonds.

A redetermination of the crystal structure of the title compound, C(6)H(16)N(2) (2+)·2Cl(-), was undertaken. All atomic coordinates including those of the H atoms were refined freely. The cation is located on a centre of symmetry. Important for the crystal structure are wavy hydrogen-bonded layers that are formed by ammonium groups and chloride anions, giving hydrogen-bonded rings.

A porous ionic/molecular crystal composed of discrete triakis tetrahedral Co(8) clusters with an ideal T(d) symmetry shows interesting magnetism and porosity.

A new scheme has been devised to represent viruses and other biological assemblies with regular noncrystallographic symmetry in the Protein Data Bank (PDB). The scheme describes existing and anticipated PDB entries of this type using generalized descriptions of deposited and experimental coordinate frames, symmetry and frame transformations. A simplified notation has been adopted to express the...

The notion of magnetic symmetry is reexamined in light of the recent observation of long-range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically ordered (periodic or quasiperiodic) crystal, given in terms of a “spin space group,” and its neutron diffraction diagram is established. In doing so, an ...

The title compound, C(17)H(20)N(4)O(2), has crystallographic inversion symmetry. In the crystal structure, inter-molecular hydrogen bonding between adjacent urea groups gives rise to infinite polymeric chains diagonally across the bc plane. With a centroid-centroid distance of 3.295 (2) Å, π-π stacking is present in the crystal along the same plane.

In the title compound, C(27)H(24)O(4), the 1,3-dioxane rings have chair conformations. The mol-ecule has non-crystallographic twofold rotation symmetry. The dihedral angle between the naphthalene ring systems is 17.96(4)° In the crystal structure, weak inter-molecular C-H⋯π inter-actions contribute to the crystal packing.