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Planigon: History, Measurement & Standards

In geometry, a planigon is a convex polygon that can fill the plane with only copies of itself (isotopic to the fundamental units of monohedral tessellations). In the Euclidean plane there are 3 regular planigons; equilateral triangle, squares, and regular hexagons; and 8 semiregular planigons; and 4 demiregular planigons which can tile the plane only…

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Planigon topic overview

The analysis highlights History, Measurement and Standards as prominent areas in the source structure around Planigon.

Related topics
51
Source areas
8
Connected nodes
59
Extracted relationships
79
Concept neighborhoods
25
Bridge connections
59

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.

Construction · 16 topics
Overview · 12 topics
History · 11 topics
Derivation of all possible planigons · 4 topics
Miscellaneous · 3 topics
Number of Dual Uniform Tilings · 3 topics
Fractalizing Dual k-Uniform Tilings · 1 topics
Higher Dual Uniform Tilings · 1 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.

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

History

Construction

Derivation of all possible planigons

Number of Dual Uniform Tilings

Higher Dual Uniform Tilings

  • Here 3-4-6-12 tiling

Fractalizing Dual k-Uniform Tilings

Miscellaneous

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.

How Planigon connects Entity context

The extracted context around Planigon shows recurring relationship patterns in the source. For example, Planigon → Alekseĭ Vasilʹevich, Archimedean, Branko Grünbaum, Catalan, Each, Fritz Laves, In, John Conway, Laves, Shubnikov, The, The Laves, Their, They're, This, Three, Tilings Another extracted example is Planigon → Akad, Alexander Korobov, Delone, Izv, Mat, Nauk SSSR Ser, September, Theory. Use these groups to spot repeated connection types before inspecting the individual relationships.

Planigon

Top relations

related to history · 17
Planigon → Alekseĭ Vasilʹevich, Archimedean, Branko Grünbaum, Catalan, Each, Fritz Laves, In, John Conway, Laves, Shubnikov, The, The Laves, Their, They're, This, Three, Tilings
related to References · 8
Planigon → Akad, Alexander Korobov, Delone, Izv, Mat, Nauk SSSR Ser, September, Theory
related to Regular Vertices · 7
Planigon → All, All Laves, Grünbaum, In, In Tilings, Laves, Patterns
related to Big Fractalization · 6
Planigon → By, DB, DC, In, S2TC, The
related to Planigons in the plane · 5
Planigon → By, If, In, Laves Tiling, Only
related to Optimized Tilings · 4
Planigon → Also, Catalaves, Finally, If
related to Other Edge-Edge Construction Comparisons · 4
Planigon → All, Other, Pictured, Rotates
related to Circle Packing · 3
Planigon → Below, Each, Optimized Tilings
related to Large Fractalization · 3
Planigon → To, V3, V32
related to Number of Dual Uniform Tilings · 3
Planigon → Every, If, Such

Important terminology

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

Important terminology

tilings regular planigons dual vertex uniform tiling edges laves displaystyle polygons vertices number two plane types shown k-uniform tiles must

Planigon relationships Subject–Predicate–Object triples

TTTA extracted 79 structured relationships around Planigon. Examples in this analysis include Planigon → is a → convex polygon that can fill the plane with only copies of itself and Planigon → related to 2-Dual-Uniform → There. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Planigonis aconvex polygon that can fill the plane with only copies of itself0.90text
Planigonrelated to 2-Dual-UniformThere0.60section
Planigonrelated to 2-Dual-UniformKrotenheerdt Duals0.60section
Planigonrelated to 3-Dual-UniformThere0.60section
Planigonrelated to 3-Dual-UniformKrotenheerdt Duals0.60section
Planigonrelated to 4-Dual-UniformThere0.60section
Planigonrelated to 4-Dual-UniformKrotenheerdt Duals0.60section
Planigonrelated to 5-Dual-UniformThere0.60section
Planigonrelated to 5-dual-uniform 4-Catalaves tilingsChanges0.60section
Planigonrelated to Affine Linear ExpansionsBelow0.60section
Planigonrelated to Affine Linear ExpansionsThe0.60section
Planigonrelated to Big FractalizationBy0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Planigon bring nearby vocabulary together. In this analysis, examples include Two, Angles and Plane. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • euclidean plane
    • Semiregular
    • Made
    • Circle
    • Duals
    • Original
    • Planigon
    • Planigons
    • Regular
    • Construction
    • Degree
    • Polygon
    • Triangle
  • regular hexagons
    • Polygons
    • Tilings
    • Vertex
    • Displaystyle
    • Laves
    • Vertices
    • Edges
    • Uniform
    • Every
    • K-uniform
    • Shown
    • Dual
  • dual tilings
    • Dual
    • Tilings
    • Tiling
    • Uniform
    • Planigons
    • Laves
    • Vertex
    • Vertices
    • Every
    • Shown
    • K-uniform
    • Regular
  • regular polygons
    • Must
    • Polygons
    • Regular
    • Tilings
    • Vertex
    • Displaystyle
    • Laves
    • Two
    • Vertices
    • Edges
    • Uniform
    • Degree
  • tilings and patterns
    • Dual
    • Uniform
    • Laves
    • Vertex
    • Vertices
    • Tiling
    • K-uniform
    • Polygons
    • Duals
    • Called
    • Using
    • Shown
  • regular dodecagons
    • Polygons
    • Tilings
    • Vertex
    • Displaystyle
    • Laves
    • Vertices
    • Edges
    • Uniform
    • Every
    • K-uniform
    • Shown
    • Dual
  • optimized tilings
    • Dual
    • Uniform
    • Laves
    • Vertex
    • Vertices
    • Tiling
    • K-uniform
    • Polygons
    • Duals
    • Called
    • Using
    • Shown
  • derivation of all possible planigons
    • Tilings
    • Tiling
    • Dual
    • Vertex
    • Uniform
    • Laves
    • Types
    • Vertices
    • Regular
    • Number
    • Displaystyle
    • Semiregular

Connections between topic areas Semantic bridges

For Planigon, one of the stronger structural bridges in this analysis connects Planigon with Construction. 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
Planigon — Construction · splits 43 ⟂ 17
Planigon — Overview · splits 47 ⟂ 13
Planigon — History · splits 48 ⟂ 12
Planigon — Derivation of all possible planigons · splits 55 ⟂ 5
Planigon — Number of Dual Uniform Tilings · splits 56 ⟂ 4
Planigon — Miscellaneous · splits 56 ⟂ 4

Map overview Semantic statistics

Planigon

Nodes60
Edges59
Triples79
Avg. degree1.97
Density0.033333
Components1

Source & methodology

TTTA analyzes the structure around Planigon to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, Measurement & Standards, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Planigon · EN edition · Analysis: TopicsToTalkAbout

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