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This Review provides the first comprehensive overview of the structure and properties of exotic sp 3 -crystalline aperiodic cyclic multiply twinned nano- (10-100 nm ) and meso- (up to 1 mm ) diamond particles (MTPs) exhibiting pentagonal symmetry. It spans their independent experimental discoveries (1963, 1964, 1972, and 1983) and theoretical structural insights (1993) to recent advancements. The Review focuses on high-symmetry MTPs formed by the fusion of multiple cubic diamond fragments through [111] facets. The sp 3 diamond lattice of individual fragments offers a vast range of MTP varieties. These particles are shown to be a special case of aperiodic crystalline solids with limited dimensions and rotational symmetry, leading to a breakdown of translational invariance. Detailed mathematical analysis of the MTPs' lattices highlights the crucial role of central cores in determining the symmetry and effective dimensions of these structures. Both structural and kinetic aspects of the formation mechanisms of pentagonal diamond particles are considered, revealing the main role of embryo seeds (low fullerenes, polyhexacyclo[5.5.1.1 2,6 .1 8,12 .0 3,11 .0 5,9 ]pentadecane (C 15 ), and polyheptacyclo[5.5.1.1 2,7 .1 9,14 .0 3,13 .0 6,11 ]octadecane (C 18 )) in determining the MTPs' symmetry and structure. The effective dimensions of multiply twinned diamonds are shown to be limited by structural stress caused by the mismatch of perfect pentagonal and tetrahedral dihedral angles. The extraordinary mechanical and electronic properties of multiply twinned diamonds are discussed, highlighting that hexagonal interfaces between cubic diamond fragments may determine exceptional ultrahard and quantum characteristics. The MTP X-ray diffraction spectra reveal clear pentagonal patterns with single (diamond decahedrons or dodecahedrons) or ten (diamond icosahedra) central 5-fold axes. A comparative analysis of experimental structural data and simulations at different theoretical levels demonstrates a perfect correspondence of theoretical models with crystalline lattices.

Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions' chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases.