Wallpaper Groups Research Articles

The Uniqueness of the Medieval Persian Art

I examine the symmetry used in the ornamentation of various medieval civilizations and interpret it as a characteristic feature of each cultural group. I first classify the symmetries according to the 17 wallpaper groups of crystallography, then determine their frequency and apply statistical methods to obtain quantitative and comparative information for each of these groups. The calculations show that the civilizations can be divided into two groups according to their habits: the Islamic group of Seljuks and Arabs and the Greco-Roman group, which includes Armenians, the Eastern Roman Empire and the Kingdom of Andalusia. Remarkably, Persia stands out from this division with its own art movement until the 16th century.

Pola Frieze dan Pola Kertas Dinding pada Masjid Istiqlal

The beauty of Istiqlal Mosque is reflected through its architectural design. The decorative arts that adorn this mosque are generally found in elements such as doors, windows, walls, gates, and vents, which show special patterns. Such patterns can be identified through the concept of geometric symmetry, specifically Frieze Patterns and Wallpaper Patterns. The Frieze pattern is a subgroup within a symmetry group formed through one-way translation, creating a linear pattern that repeats in one direction. There are seven types of frieze patterns, each formed through a combination of specific isometries. Along with that, there are also other geometric patterns known as wallpaper patterns. Wallpaper patterns analyze patterns based on transformations on a flat plane and have seventeen types. This study aims to explore and explain geometric patterns based on Frieze Patterns and Wallpaper Patterns contained in the decorative arts of Istiqlal Mosque. Data collection methods involve observation and documentation. The results showed that there are certain frieze patterns in the Istiqlal Mosque, such as the type . Meanwhile, the wallpaper patterns identified in the design of the Istiqlal Mosque are type pmm and pmg. It is important to note that not all designs in the decorative arts of Istiqlal Mosque can be categorized into seven frieze patterns as well as seventeen wallpaper patterns.

The Uniqueness of the Medieval Persian Art

I examine the symmetry used in the ornamentation of various medieval civilizations and interpret it as a characteristic feature of each cultural group. I first classify the symmetries according to the 17 wallpaper groups of crystallography, then determine their frequency and apply statistical methods to obtain quantitative and comparative information for each of these groups. The calculations show that the civilizations can be divided into two groups according to their habits: the Islamic group of Seljuks and Arabs and the Greco-Roman group, which includes Armenians, the Eastern Roman Empire and the Kingdom of Andalusia. Remarkably, Persia stands out from this division with its own art movement until the 16th century.

The Uniqueness of the Medieval Persian Art

I examine the symmetry used in the ornamentation of various medieval civilizations and interpret it as a characteristic feature of each cultural group. I first classify the symmetries according to the 17 wallpaper groups of crystallography, then determine their frequency and apply statistical methods to obtain quantitative and comparative information for each of these groups. The calculations show that the civilizations can be divided into two groups according to their habits: the Islamic group of Seljuks and Arabs and the Greco-Roman group, which includes Armenians, the Eastern Roman Empire and the Kingdom of Andalusia. Remarkably, Persia stands out from this division with its own art movement until the 16th century.

Equivariant K-Homology and K-Theory for Some Discrete Planar Affine Groups

Abstract We consider the semi-direct products $G={\mathbb{Z}}^{2}\rtimes GL_{2}({\mathbb{Z}}), {\mathbb{Z}}^{2}\rtimes SL_{2}({\mathbb{Z}})$, and ${\mathbb{Z}}^{2}\rtimes \Gamma (2)$ (where $\Gamma (2)$ is the congruence subgroup of level 2). For each of them, we compute both sides of the Baum–Connes conjecture, namely the equivariant $K$-homology of the classifying space $\underline{E}G$ for proper actions on the left-hand side, and the analytical K-theory of the reduced group $C^{*}$-algebra on the right-hand side. The computation of the LHS is made possible by the existence of a 3-dimensional model for $\underline{E}G$, which allows to replace equivariant K-homology by Bredon homology. We pay due attention to the presence of torsion in $G$, leading to an extensive study of the wallpaper groups associated with finite subgroups. For the first and third groups, the computations in $K_{0}$ provide explicit generators that are matched by the Baum–Connes assembly map.

Drawn from Nature: Wallpaper patterns in New Zealand's Schools of Art and Design

Schools of art and design were established in New Zealand from 1870 to foster the development of technical skills in the trades and the creative and decorative arts. These schools flourished throughout the latter two decades of the nineteenth century and the early decades of the twentieth century. Informed by the teachings of the South Kensington School in England, students in New Zealand were instructed in the design of patterns for interior finishes, such as wallpapers, tiles, linoleum and textiles. The blossoming Arts and Crafts movement not only guided the teaching models of these schools, but encouraged students to explore the graphic possibilities of flora and fauna, which in the New Zealand context resulted in original decorative patterns with native motifs.
 This paper will explore the design of wallpaper patterns by students at the New Zealand schools of art, focusing on those produced between the mid-1880s and the late 1890s. The influence and inspiration for these patterns will be traced, from the Arts and Crafts movement, the teaching methods at schools of art and design, to the natural New Zealand environment.

Bezemelerin Simetrilerinde Saklı Olan Ortaçağ Kültür İlişkileri

We trace the culture on the mosaics of seven medieval civilizations by taking the symmetry of the ornaments found on the mosaics as characteristic evidence for the cultural group in which the artwork is created. We classify the ornaments into 17 wallpaper groups according to their symmetry. Applying the cosine law to the frequency of each symmetry group we calculate the pairwise correlation of the cultural interactions. Finally, a hierarchical cluster analysis is performed on the correlations to find cultural groups that are closely related to each other. The results show the formation of two clusters: The Islamic cluster includes the Arabs and the Seljuk dynasties. The Hellenistic group inspired other Anatolian civilizations and even influenced the Umayyads in Andalusia. These results are consistent with the calculations based on multidimensional scaling. Our work demonstrates the possibility of applying symmetry analysis and statistical methods to the visual arts to reveal valuable details such as the hidden influences in art practice.

To slip out of the geometric straitjacket

The tunnel method is a technique employed in the design of wallpaper patterns to facilitate the hanging process while maintaining the integrity of the pattern. It can be utilised in both the reconstruction of historical patterns and the creation of new ones. I have explored the potential of this method since 2006, and in my latest project, I had the opportunity to document its application in Swedish wallpaper studios and endeavour to understand its historical background regarding cultural and printing conditions. By testing the effect of applying the method to wallpaper patterns, I explored its possibility of generating distinctive effects within the pattern when the wallpaper is installed. In this way, the user can actively participate in determining the degree of variation in the pattern during the installation process, either by embracing serendipity or by making deliberate choices. The purpose is to promote wallpaper patterns with greater variation and wallpapers made from sustainable materials. Although this investigation led to several different ways of utilising the tunnel method, there is still much to be explored in this field. By sharing my work, I aim to motivate more people to explore the potential of the tunnel method. Notably, the communication of its functionality to customers and its integration within the cultural context remain limited.

Symmetry Perception and Psychedelic Experience

This review of symmetry perception has six parts. Psychophysical studies have investigated symmetry perception for over 100 years (part 1). Neuroscientific studies on symmetry perception have accumulated in the last 20 years. Functional MRI and EEG experiments have conclusively shown that regular visual arrangements, such as reflectional symmetry, Glass patterns, and the 17 wallpaper groups all activate the extrastriate visual cortex. This activation generates an event-related potential (ERP) called sustained posterior negativity (SPN). SPN amplitude scales with the degree of regularity in the display, and the SPN is generated whether participants attend to symmetry or not (part 2). It is likely that some forms of symmetry are detected automatically, unconsciously, and pre-attentively (part 3). It might be that the brain is hardwired to detect reflectional symmetry (part 4), and this could contribute to its aesthetic appeal (part 5). Visual symmetry and fractal geometry are prominent in hallucinations induced by the psychedelic drug N,N-dimethyltryptamine (DMT), and visual flicker (part 6). Integrating what we know about symmetry processing with features of induced hallucinations is a new frontier in neuroscience. We propose that the extrastriate cortex can generate aesthetically fascinating symmetrical representations spontaneously, in the absence of external symmetrical stimuli.

Hall effect of ferro/antiferromagnetic wallpaper fermions

Nonsymmorphic crystals can host characteristic double surface Dirac cones with fourfold degeneracy on the Dirac points, called wallpaper fermion, protected by wallpaper group symmetry. We clarify the charge and spin Hall effect of wallpaper fermions in the presence of the (anti)ferromagnetism. Based on a four-sublattice model, we construct the effective Hamiltonian of wallpaper fermions coupled with the ferromagnetic or antiferromagnetic moment. Both ferromagnetic and antiferromagnetic moments induce an energy gap for the wallpaper fermions, leading to quantized (spin) Hall conductivity. The ferromagnetic wallpaper fermion induces the Hall conductivity quantized into ${e}^{2}/h$, which is twice that for a single Dirac fermion on the surface of topological insulators. On the other hand, the spin Hall conductivity decays and reaches to be a finite value as the antiferromagnetic coupling increases. We also show that the results above are valid for a general model of wallpaper fermions from symmetry consideration.

An “Artistic Display of Wares”: The Wallpaper Trade During Otago’s Goldrush, 1860-1867

ABSTRACT In comparison with interior design and architecture studies in Britain, Europe, the United States and Australia, little research has been conducted on interiors of the 19th century in New Zealand. Publications on New Zealand’s architectural heritage have largely focused on house exteriors, often including only passing reference to components of interior design. The fragments of knowledge about New Zealand’s early interiors that emerge from existing literature provide insight into the web of factors that shaped them. These include socio-cultural factors, the influence of media, and global and local economies. Picking up on these themes, this paper focuses on the wallpaper trade in Otago prior to, during and following the goldrush, between 1860 and 1867. The picture that emerges is of an Antipodean trade in predominantly British wallpapers, and a trans-Tasman network that facilitated the flow of wallpapers and traders between the Australian colony of Victoria and the province of Otago in New Zealand. Insights into the wallpaper patterns available in 1860s Dunedin are provided by photographs of shop windows and the display of wallpapers in the Furniture Court of the 1865 New Zealand Exhibition, as well as an archaeological sample from the 1860s.

Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators

Topological crystalline insulators (TCIs) can host anomalous surface states which inherits the characteristics of crystalline symmetry that protects the bulk topology. Especially, the diversity of magnetic crystalline symmetries indicates the potential for novel magnetic TCIs with distinct surface characteristics. Here, we propose a topological magnetic Dirac insulator (TMDI), whose two-dimensional surface hosts fourfold-degenerate Dirac fermions protected by either the {p}_{c}^{{prime} }4mm or p{4}^{{prime} }{g}^{{prime} }m magnetic wallpaper group. The bulk topology of TMDIs is protected by diagonal mirror symmetries, which give chiral dispersion of surface Dirac fermions and mirror-protected hinge modes. We propose candidate materials for TMDIs including Nd4Te8Cl4O20 and DyB4 based on first-principles calculations, and construct a general scheme for searching TMDIs using the space group of paramagnetic parent states. Our theoretical discovery of TMDIs will facilitate future research on magnetic TCIs and illustrate a distinct way to achieve anomalous surface states in magnetic crystals.

Densest packing of flexible polymers in 2D films.

How dense objects, particles, atoms, and molecules can be packed is intimately related to the properties of the corresponding hosts and macrosystems. We present results from extensive Monte Carlo simulations on maximally compressed packings of linear, freely jointed chains of tangent hard spheres of uniform size in films whose thickness is equal to the monomer diameter. We demonstrate that fully flexible chains of hard spheres can be packed as efficiently as monomeric analogs, within a statistical tolerance of less than 1%. The resulting ordered polymer morphology corresponds to an almost perfect hexagonal triangular (TRI) crystal of the p6m wallpaper group, whose sites are occupied by the chain monomers. The Flory scaling exponent, which corresponds to the maximally dense polymer packing in 2D, has a value of ν = 0.62, which lies between the limits of 0.50 (compact and collapsed state) and 0.75 (self-avoiding random walk).

Orbifold jacket

The author discusses orbifold signatures for the 17 wallpaper patterns. Fabric is created using each of the wallpaper patterns and sewn into a fashion show kimono. The resulting reversible wallpaper jacket has orbifold signatures on each of the patterns and 10 samples of folded orbifolds as embellishments.

Symmetry-engineered nodal lines and hourglass fermions in patterned two-dimensional electron gas

In most cases, the formation of topological quantum states requires intrinsic crystalline symmetry to protect either discrete or continuous degeneracies in real materials, which greatly hinders their realization in practice. Patterned two-dimensional electron gas (2DEG), on the other hand, has become a very effective external means to manipulate the symmetry to whatever we want. Here, taking nonsymmorphic symmetries as the focus of attention, based on patterned 2DEG decoration, we reveal rich band-crossing features in two-dimensional systems. It is demonstrated that in the presence of intrinsic spin-orbital coupling (SOC), wallpaper groups $p2mg,p2gg$, and $p4mg$ possess fourfold-degenerate Dirac nodal lines, and if Rashba SOC is further considered, the fourfold-degenerate nodal lines disappear and hourglass Weyl fermions then emerge. Our results not only afford an attractive route for designing robust nodal-line and hourglass Weyl semimetals in reality, but also pave the way for designing ideal macroscale materials through rational extrinsic symmetry engineering.

Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice

Non-symmorphic symmetries protect Dirac nodal lines and cones in lattice systems. Here, we investigate the spectral properties of a two-dimensional lattice belonging to a non-symmorphic group. Specifically, we look at the herringbone lattice, characterized by two sets of glide symmetries applied in two orthogonal directions. We describe the system using a nearest-neighbor tight-binding model containing horizontal and vertical hopping terms. We find two nonequivalent Dirac cones inside the first Brillouin zone along a high-symmetry path. We tune these Dirac cones’ positions by breaking the lattice symmetries using on-site potentials. These Dirac cones can merge into a semi-Dirac cone or unfold along a high-symmetry path. Finally, we perturb the system by applying a dimerization of the hopping terms. We report a flow of Dirac cones inside the first Brillouin zone describing quasi-hyperbolic curves. We present an implementation in terms of CO atoms placed on the top of a Cu(111) surface.

Classification of time-reversal-invariant crystals with gauge structures

A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain largely unexplored. Despite recent advances in artificial crystals, whose intrinsic gauge structures necessarily require a projective description, a unified theory is yet to be established. Here, we establish such a unified theory by exhaustively classifying and representing all 458 projective symmetry algebras of time-reversal-invariant crystals from 17 wallpaper groups in two dimensions-189 of which are algebraically non-equivalent. We discover three physical signatures resulting from projective symmetry algebras, including the shift of high-symmetry momenta, an enforced nontrivial Zak phase, and a spinless eight-fold nodal point. Our work offers a theoretical foundation for the field of artificial crystals and opens the door to a wealth of topological states and phenomena beyond the existing paradigms.

Symmetries in Power Electronics and Lattice Converters

The past 50 years witnessed the inventions of more than one thousand power electronic topologies. However, we still lack a common standard to compare and classify various topologies. Moreover, topologies are often created through intuition rather than systematic approaches. The intuition of voltage and current sharing, along with modularity and scalability, gives rise to cascaded-bridge and multi-parallleled converters, respectively. Nevertheless, power converters with both high-voltage and large-current capabilities are still obscure yet important. This article first investigates the symmetries of circuit topologies through group theory. Notably, symmetries lie in twofold—individual modules and connections. Symmetries not only help to classify topologies but also play an important role in the creation of new topologies. Based on wallpaper groups, this article proposes the lattice converters, which readily scale to manage high voltages and large currents. The proposed lattice converters benefit from 1) modularity and scalability, 2) boundless current and voltage ratings, 3) multiple input/output ports, 4) sensorless voltage balancing, 5) high power quality, and 6) flexible control. Simulation and experimental results demonstrate the effectiveness and superiority of the proposed theory and lattice converters.

Classification of wallpaper patterns and features of their compositional structure

Classification of wallpaper patterns and features of their compositional structure

Generalized fermion doubling theorems: Classification of two-dimensional nodal systems in terms of wallpaper groups

The Nielsen-Ninomiya Theorem has set up a ground rule for the minimal number of the topological points in a Brillouin zone. Notably, in the 2D Brillouin zone, chiral symmetry and space-time inversion symmetry can properly define topological invariants as charges characterizing the stability of the nodal points so that the non-zero charges protect these points. Due to the charge neutralization, the Nielsen-Ninomiya Theorem requires at least two stable topological points in the entire Brillouin zone. However, additional crystalline symmetries might duplicate the points. In this regard, for the wallpaper groups with crystalline symmetries, the minimal number of the nodal points in the Brillouin zone might be more than two. In this work, we determine the minimal numbers of the nodal points for the wallpaper groups in chiral-symmetric and space-time-inversion-symmetric systems separately and provide examples for new topological materials, such as topological nodal time-reversal-symmetric superconductors and Dirac semimetals. This generalized Nielsen-Ninomiya Theorem serves as a guide to search for 2D topological nodal materials and new platforms for twistronics. Furthermore, we show the Nielsen-Ninomiya Theorem can be extended to 2D non-Hermitian systems hosting topologically protected exceptional points and Fermi points for the 17 wallpaper groups and use the violation of the theorem on the surface to classify 3D Hermitian and non-Hermitian topological bulks.