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Vertex configuration: All uniform vertex configurations of regular convex polygons, Face configuration & Star polygons

In geometry, a vertex configuration is a shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex. It has variously been called a vertex description, vertex type, vertex symbol, vertex arrangement, vertex pattern, face-vector, vertex sequence. It is also called a Cundy and Rollett symbol for its usage for the…

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Vertex configuration topic overview

The analysis highlights All uniform vertex configurations of regular convex polygons, Face configuration and Star polygons as prominent areas in the source structure around Vertex configuration.

Related topics
60
Source areas
5
Connected nodes
65
Extracted relationships
7
Related term clusters
41
Bridge connections
65

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.

All uniform vertex configurations of regular convex polygons · 31 topics
Overview · 13 topics
Face configuration · 7 topics
Star polygons · 6 topics
Notation · 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

Notation

Star polygons

All uniform vertex configurations of regular convex polygons

Face configuration

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Vertex configuration connects Entity context

The extracted context around Vertex configuration shows recurring relationship patterns in the source. For example, Vertex configuration → Hence, Schläfli, The Schläfli Another extracted example is Vertex configuration → NOTE, Semiregular. Use these groups to spot repeated connection types before inspecting the individual relationships.

Vertex configuration

Top relations

related to Notation · 3
Vertex configuration → Hence, Schläfli, The Schläfli
related to All uniform vertex configurations of regular convex polygons · 2
Vertex configuration → NOTE, Semiregular
is a · 1
Vertex configuration → shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex
related to Star polygons · 1
Vertex configuration → Schläfli

Important terminology

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

Important terminology

vertex configuration notation faces polyhedra example symbol regular uniform face number tilings also tiling vertices defect around polyhedron dodecahedron figure

Vertex configuration relationships Subject–Predicate–Object triples

TTTA extracted 7 structured relationships around Vertex configuration. Examples in this analysis include Vertex configuration → is a → shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex and Vertex configuration → related to All uniform vertex configurations of regular convex polygons → Semiregular. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Vertex configurationis ashorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex0.90text
Vertex configurationrelated to All uniform vertex configurations of regular convex polygonsSemiregular0.60section
Vertex configurationrelated to All uniform vertex configurations of regular convex polygonsNOTE0.60section
Vertex configurationrelated to NotationSchläfli0.60section
Vertex configurationrelated to NotationThe Schläfli0.60section
Vertex configurationrelated to NotationHence0.60section
Vertex configurationrelated to Star polygonsSchläfli0.60section

Related concept clusters Related term clusters

The concept neighborhoods around Vertex configuration bring nearby vocabulary together. In this analysis, examples include Vertex, Polyhedron and Dodecahedron. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Vertex configuration
    • Vertex
    • Polyhedron
    • Dodecahedron
    • Uniform
    • Defines
    • Figure
    • Tiling
    • Regular
    • Chiral
    • Icosidodecahedron
    • Notation
    • One
  • vertex configuration
    • Vertex
    • Polyhedron
    • Dodecahedron
    • Uniform
    • Defines
    • Figure
    • Tiling
    • Regular
    • Chiral
    • Icosidodecahedron
    • Notation
    • One
  • faces
    • Vertex
    • Alternating
    • Notation
    • Face
    • One
    • Pentagons
    • Triangles
    • Polyhedron
    • Represents
    • Therefore
    • Sides
    • Around
  • uniform polyhedra
    • Uniform
    • Chiral
    • Defect
    • Angle
    • Face
    • Vertex
    • Regular
    • Vertices
    • Number
    • Example
    • Defines
    • Different
  • regular polyhedra
    • Star
    • Uniform
    • Defect
    • Semiregular
    • Angle
    • Tiling
    • Vertex
    • Tilings
    • Regular
    • Vertices
    • Example
    • Number
  • semiregular polyhedra
    • Uniform
    • Defect
    • Tiling
    • Angle
    • Vertex
    • Solids
    • Regular
    • Vertices
    • Example
    • Number
    • Chiral
    • Defines
  • notation
    • Face
    • Faces
    • Star
    • Around
    • Regular
    • Number
    • Chiral
    • Different
    • Polygons
    • Vertex
    • Represents
    • Schläfli
  • all uniform vertex configurations of regular convex polygons
    • Star
    • Regular
    • Chiral
    • Semiregular
    • Face
    • Tiling
    • Defect
    • One
    • Polygons
    • Tilings
    • Uniform
    • Vertices

Connections between topic areas Semantic bridges

For Vertex configuration, one of the stronger structural bridges in this analysis connects Vertex configuration with All uniform vertex configurations of regular convex polygons. 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
Vertex configuration — All uniform vertex configurations of regular convex polygons · splits 34 ⟂ 32
Vertex configuration — Overview · splits 52 ⟂ 14
Vertex configuration — Face configuration · splits 58 ⟂ 8
Vertex configuration — Star polygons · splits 59 ⟂ 7
Vertex configuration — Notation · splits 62 ⟂ 4

Map overview Semantic statistics

Vertex configuration

Nodes66
Edges65
Triples7
Avg. degree1.97
Density0.030303
Components1

Source & methodology

TTTA analyzes the structure around Vertex configuration to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as All uniform vertex configurations of regular convex polygons, Face configuration & Star polygons, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Vertex configuration · EN edition · Analysis: TopicsToTalkAbout

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