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Explore the main themes, entities and connections around Wallpaper group. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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The seventeen groups
75 related topics
Formal definition and discussion
Topologically discreteLinearly independentIsometry groupsThe same up to an affine transformation of the planeRotational symmetry
18 related topics
Overview
31 related topics
Web demo and software
7 related topics
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Symmetries Symmetry
- Architecture
- Decorative art
- Textiles Textile
- Tiles Tile
- Wallpaper
- Tahiti
- Nineveh
- Assyria
- Porcelain
- China
- Pmg Wallpaper group
- IUCr notation International Union of Crystallography
- Orbifold notation
- Frieze groups Frieze group
- Space groups Space group
- Proof Mathematical proof
- Groups Group (mathematics)
- Evgraf Fedorov Yevgraf Fyodorov
- George Pólya
- Carl Hermann
- Charles-Victor Mauguin
- Primitive cell
- John Conway John Horton Conway
- Orbifold
- Cyclic Point group
- Dihedral Dihedral group
- Coxeter
- Bracket notation Coxeter notation
- Coxeter groups Coxeter group
Symmetries of patterns
- Translational symmetry
- Translation Translation (geometry)
- Euclidean plane isometries Euclidean plane isometry
- Rotation
- Reflection Reflection (mathematics)
- Glide reflection
Formal definition and discussion
- Topologically discrete Discrete space
- Linearly independent
- Isometry groups Isometry group
- The same up to an affine transformation of the plane Conjugation of isometries in Euclidean space
- Rotational symmetry
- Orientation Orientation (mathematics)
- Two-dimensional discrete point groups Symmetry group
- Vector Vector (geometry)
- Displacement Displacement (vector)
- Rotations Rotation (mathematics)
- Rational number
- Crystallographic restriction theorem
- Polygon
- Sphere
- Hyperbolic plane Hyperbolic geometry
- Euler characteristic
- Order Order (group theory)
- Bad Bad orbifold?action=edit&redlink=1
The seventeen groups
- Fundamental domain
- Lattice Lattice (group)
- Medieval
- Diapering
- Co-uniform Planigon
- Sandwich Islands Hawaiian Islands
- Hawaii
- Egyptian Ancient Egypt
- Tomb
- Wire fence Chain-link fencing
- Biban el Moluk
- Thebes Thebes (Egypt)
- Indian India
- Great Exhibition
- Herringbone pattern
- Salzburg
- Snub square tiling
- Elongated triangular tiling
- Amun
- Abu Simbel
- Dado Dado (architecture)
- Bronze
- Nimroud
- Spandrels Spandrel
- Arches Arch
- Alhambra
- Spain
- Soffit
- Persian Persian empire
- Tapestry
Lattice types
- Bravais lattices Bravais lattice
Symmetry groups
- Degrees of freedom Degrees of freedom (physics and chemistry)
Dependence of wallpaper groups on transformations
- Scaling Scaling (geometry)
- Similarity transformations Similarity (geometry)
- Affine transformations Affine transformation
Web demo and software
Advanced semantic analysis
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Wallpaper group
Nodes151
Edges150
Triples86
Avg. degree1.99
Density0.013245
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Wallpaper group
Top relations
related to Web demo and software · 20
Wallpaper group → Adobe Illustrator, EscherSketch, Heesch, Inkscape, Java, JavaScript, Kali, Kali Archived, Mac Classic, MadPattern, Repper, See, Several, SymmetryWorks, TALES GAME, The, Usually, Wallpaper Symmetry, Wayback Machine, Windows
related to Group p3m1 (*333) · 11
Wallpaper group → D3The, For, In, It, Lattice, Like, Orbifold, The, Then, There, This
related to Group p31m (3*3) · 10
Wallpaper group → D3The, For, In, It, Lattice, Like, Orbifold, Then, There, This
related to Group p3 (333) · 8
Wallpaper group → C3The, For, Imagine, In, Lattice, Orbifold, Then, This
related to Dependence of wallpaper groups on transformations · 7
Wallpaper group → It, Note, Reflection, Rotational, Such, The, Translational
related to Lattice types · 7
Wallpaper group → Bravais, In, It, Special, The, There, They
related to Why there are exactly seventeen groups · 7
Wallpaper group → An, Because, Euler, If, Reversing, The, When
related to Formal definition and discussion · 5
Wallpaper group → Euclidean, Mathematically, The, Thus, Two
related to The independent translations condition · 5
Wallpaper group → In, R2, The, Tv, Tw
related to Symmetry groups · 4
Wallpaper group → The, There, These, Wallpaper
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Important terminology
group symmetry wallpaper rotation orbifold groups lattice reflection two reflections order one notation pattern glide centres point translation translations plane
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Wallpaper group | related to Dependence of wallpaper groups on transformations | The | 0.60 | section |
| Wallpaper group | related to Dependence of wallpaper groups on transformations | Translational | 0.60 | section |
| Wallpaper group | related to Dependence of wallpaper groups on transformations | Rotational | 0.60 | section |
| Wallpaper group | related to Dependence of wallpaper groups on transformations | Reflection | 0.60 | section |
| Wallpaper group | related to Dependence of wallpaper groups on transformations | It | 0.60 | section |
| Wallpaper group | related to Dependence of wallpaper groups on transformations | Note | 0.60 | section |
| Wallpaper group | related to Dependence of wallpaper groups on transformations | Such | 0.60 | section |
| Wallpaper group | related to Formal definition and discussion | Mathematically | 0.60 | section |
| Wallpaper group | related to Formal definition and discussion | Euclidean | 0.60 | section |
| Wallpaper group | related to Formal definition and discussion | Two | 0.60 | section |
| Wallpaper group | related to Formal definition and discussion | Thus | 0.60 | section |
| Wallpaper group | related to Formal definition and discussion | The | 0.60 | section |
No triples extracted yet.
Related concept clusters Concept neighborhoods
Clusters of nearby vocabulary surrounding the topic. Scan them for adjacent concepts and language you may have missed.These clusters group vocabulary that occurs around closely connected concepts in the source material.
Connections between topic areas Semantic bridges
Bridge nodes connect otherwise separate parts of the map. Expand a row to inspect the topic groups on each side.Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.
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