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Uniform tilings in hyperbolic plane: Standards, Right triangle domains & Wythoff construction

In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices…

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Uniform tilings in hyperbolic plane topic overview

The analysis highlights Standards, Right triangle domains and Wythoff construction as prominent areas in the source structure around Uniform tilings in hyperbolic plane.

Related topics
52
Source areas
6
Connected nodes
58
Related term clusters
28
Bridge connections
58

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 16 topics
Right triangle domains · 13 topics
Wythoff construction · 10 topics
General triangle domains · 6 topics
Quadrilateral domains · 4 topics
Ideal triangle domains · 3 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Wythoff construction

Right triangle domains

General triangle domains

Quadrilateral domains

Ideal triangle domains

For the semantics nerds

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Advanced semantic analysis

How Uniform tilings in hyperbolic plane connects Entity context

See recurring relationship patterns around Uniform tilings in hyperbolic plane before inspecting the individual extracted relationships.

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

uniform tilings triangle orbifold group coxeter contains hyperbolic tiling regular vertex families fundamental ideal symmetry also polygons domains right vertices

Uniform tilings in hyperbolic plane relationships Subject–Predicate–Object triples

TTTA extracted structured relationships around Uniform tilings in hyperbolic plane. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc

Related concept clusters Related term clusters

The concept neighborhoods around Uniform tilings in hyperbolic plane bring nearby vocabulary together. In this analysis, examples include Tilings, Uniform and Contains. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Uniform tilings in hyperbolic plane
    • Tilings
    • Uniform
    • Contains
    • Triangle
    • Group
    • Orbifold
    • Coxeter
    • Regular
    • Plane
    • Ideal
    • Families
    • Faces
  • uniform tilings in hyperbolic plane
    • Tilings
    • Uniform
    • Contains
    • Group
    • Coxeter
    • Orbifold
    • Triangle
    • Ideal
    • Vertices
    • Regular
    • Plane
    • Polygons
  • hyperbolic geometry
    • Regular
    • Plane
    • Tilings
    • Domains
    • Fundamental
    • Families
    • Uniform
    • Infinite
    • Faces
    • Quadrilateral
    • Right
    • Triangles
  • regular polygons
    • Around
    • Vertex
    • Schläfli
    • Symbol
    • Polygons
    • Regular
    • Right
    • Triangles
    • Also
    • Given
    • Snub
    • Vertices
  • tiling
    • Dual
    • Represents
    • Symmetry
    • Uniform
    • Vertex
    • Regular
    • Alternated
    • Vertices
    • Domain
    • One
    • Fundamental
    • Around
  • heptagonal tiling
    • Dual
    • Represents
    • Symmetry
    • Uniform
    • Vertex
    • Regular
    • Alternated
    • Vertices
    • Domain
    • One
    • Fundamental
    • Around
  • regular
    • Schläfli
    • Symbol
    • Polygons
    • Right
    • Triangles
    • Also
    • Tiling
    • Tilings
    • Families
    • Uniform
    • General
    • Given
  • fundamental domain triangle
    • Group
    • Orbifold
    • Contains
    • Coxeter
    • Domain
    • Fundamental
    • Uniform
    • Symmetry
    • One
    • Represents
    • Dual
    • Ideal

Connections between topic areas Semantic bridges

For Uniform tilings in hyperbolic plane, one of the stronger structural bridges in this analysis connects Uniform tilings in hyperbolic plane with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Uniform tilings in hyperbolic plane — Overview · splits 42 ⟂ 17
Uniform tilings in hyperbolic plane — Right triangle domains · splits 45 ⟂ 14
Uniform tilings in hyperbolic plane — Wythoff construction · splits 48 ⟂ 11
Uniform tilings in hyperbolic plane — General triangle domains · splits 52 ⟂ 7
Uniform tilings in hyperbolic plane — Quadrilateral domains · splits 54 ⟂ 5
Uniform tilings in hyperbolic plane — Ideal triangle domains · splits 55 ⟂ 4

Map overview Semantic statistics

Uniform tilings in hyperbolic plane

Nodes59
Edges58
Triples0
Avg. degree1.97
Density0.033898
Components1

Source & methodology

TTTA analyzes the structure around Uniform tilings in hyperbolic plane to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Standards, Right triangle domains & Wythoff construction, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Uniform tilings in hyperbolic plane · EN edition · Analysis: TopicsToTalkAbout

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