Forbidden Crystals: In crystalline materials, a unit cell is replicated in space through a series of rotations, inversions, and reflections. In order to fully fill space, only certain rotational symmetries are allowed. Quasicrystals contain aperiodic tilings of two or more basic shapes that allow these forbidden rotation symmetries. A number of quasicrystalline materials have been synthesized in the lab, including a number of aluminum alloys. Bindi et al. (p. 1306 ) examined samples of the mineral khatyrkite, with a nominal composition of (Cu,Zn)Al ₂ . A number of quasicrystalline grains with composition similar to synthetically formed materials were observed. Thus, quasicrystals can form in nature under geological conditions.

Characterizing complex microbial communities with single-cell resolution has been a long-standing goal of microbiology. We present Microbe-seq, a high-throughput method that yields the genomes of individual microbes from complex microbial communities. We encapsulate individual microbes in droplets with microfluidics and liberate their DNA, which we then amplify, tag with droplet-specific barcodes, and sequence. We explore the human gut microbiome, sequencing more than 20,000 microbial single-amplified genomes (SAGs) from a single human donor and coassembling genomes of almost 100 bacterial species, including several with multiple subspecies strains. We use these genomes to probe microbial interactions, reconstructing the horizontal gene transfer (HGT) network and observing HGT between 92 species pairs; we also identify a significant in vivo host-phage association between crAssphage and one strain of Bacteroides vulgatus . Microbe-seq contributes high-throughput culture-free capabilities to investigate genomic blueprints of complex microbial communities with single-microbe resolution.

We show that colloidal particles with attractive interactions induced by a nonadsorbing polymer exhibit a stable phase consisting of a fluid of clusters of particles. This phase persists even in the absence of any long-range repulsion due to charge, contrary to expectations based on simulation and theory. Cluster morphology depends strongly on the range of the interparticle attraction: With a shorter range, clusters are tenuous and branched; with a longer range, they are more compact.

The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (“girih tiles”) decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West.

Icosahedrite, ideally Al₆₃Cu₂₄Fe₁₃, is a new mineral from the Khatyrka River, southeastern Chukhotka, Russia. It occurs as dark gray-black anhedral to subhedral grains up to 100 μm across, closely associated with spinel, diopside, forsterite, nepheline, sodalite, corundum, stishovite, khatyrkite, cupalite, and an unnamed phase of composition AlCuFe. Icosahedrite is opaque with a metallic luster, possesses a gray streak, and is brittle with an uneven fracture. The density could not be determined. For quasicrystals, by definition, the structure is not reducible to a single three-dimensional unit cell, so neither cell parameters nor Z can be given. In plane-polarized incident light, icosahedrite exhibits neither bireflectance nor pleochroism. Between crossed polars, it is isotropic. Reflectance percentages (R_min = R_max) for the four standard COM wavelengths are 62.3 (471.1 nm), 60.6 (548.3 nm), 58.1 (586.6 nm), and 56.0 (652.3 nm), respectively. The X-ray powder pattern was indexed on the basis of six integer indices, as conventionally used with quasicrystals, where the lattice parameter (in six-dimensional notation) is measured to be a_6D = 12.64 Å, with probable space group Fm3̅ 5̅. The four strongest X-ray powder-diffraction lines [d in Å (I/I₀) (n₁,n₂,n₃,n₄,n₅,n₆)] are: 2.006 (100) (42̅0 042), 2.108 (90) (422̅ 2̅22), 1.238 (30) (604̅ 064), and 3.41 (25) (311̅ 1̅11). Average results of 34 electron-microprobe analyses gave, on the basis of total atoms = 100, the formula Al_63.11Cu_24.02Fe_12.78Si_0.03Co_0.01Ca_0.01Zn_0.01Cr_0.02Cl_0.01. The simplified formula is Al₆₃Cu₂₄Fe₁₃, which requires the mass fractions Al 43.02, Cu 38.60, Fe 18.38, total 100.00 wt%. The new mineral is named for the icosahedral symmetry of its internal atomic structure, as observed in its diffraction pattern. Both the new mineral and mineral name have been approved by the Commission on New Minerals, Nomenclature and Classification, IMA (2010-042).