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Petrie polygon: History, The Petrie polygons of the regular polyhedra & Overview

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one of the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a regular polyhedron is a skew polygon such that every two consecutive sides (but no three) belongs to one of…

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Petrie polygon topic overview

The analysis highlights History, The Petrie polygons of the regular polyhedra and Overview as prominent areas in the source structure around Petrie polygon.

Related topics
43
Source areas
5
Connected nodes
48
Extracted relationships
41
Concept neighborhoods
26
Bridge connections
48

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 · 18 topics
The Petrie polygons of the regular polyhedra · 13 topics
History · 7 topics
The Petrie polygon of regular polychora (4-polytopes) · 3 topics
The Petrie polygon projections of regular and uniform polytopes · 2 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

The Petrie polygons of the regular polyhedra

The Petrie polygon of regular polychora (4-polytopes)

The Petrie polygon projections of regular and uniform polytopes

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 Petrie polygon connects Entity context

The extracted context around Petrie polygon shows recurring relationship patterns in the source. For example, Petrie polygon → Abstract Regular Polytopes, Cambridge University Press, Chapter, Coxeter, Dover, Dover Publications, Egon Schulte, Essays, Flags, Geometry, ISBN, LCCN, Mathematical Recreations, McMullen, New York, Orthoschemes, Petrie, Petrie Polygons, Regular, Regular Polytopes Another extracted example is Petrie polygon → In, Kepler, Petrie, Poinsot, The, The Petrie. Use these groups to spot repeated connection types before inspecting the individual relationships.

Petrie polygon

Top relations

related to Further reading · 25
Petrie polygon → Abstract Regular Polytopes, Cambridge University Press, Chapter, Coxeter, Dover, Dover Publications, Egon Schulte, Essays, Flags, Geometry, ISBN, LCCN, Mathematical Recreations, McMullen, New York, Orthoschemes, Petrie, Petrie Polygons, Regular, Regular Polytopes
related to The Petrie polygons of the regular polyhedra · 6
Petrie polygon → In, Kepler, Petrie, Poinsot, The, The Petrie
related to External links · 4
Petrie polygon → Eric, MathWorld, Petrie, Weisstein
related to The Petrie polygon of regular polychora (4-polytopes) · 3
Petrie polygon → As, Petrie, The Petrie
related to Hypercubes · 2
Petrie polygon → Petrie, So
related to The Petrie polygon projections of regular and uniform polytopes · 1
Petrie polygon → The Petrie

Important terminology

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

Important terminology

petrie regular polygon polygons polytopes coxeter sides skew every one surface faces consecutive polyhedra also dual polytope belongs plane graph

Petrie polygon relationships Subject–Predicate–Object triples

TTTA extracted 41 structured relationships around Petrie polygon. Examples in this analysis include Petrie polygon → related to External links → Weisstein and Petrie polygon → related to External links → Eric. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Petrie polygonrelated to External linksWeisstein0.60section
Petrie polygonrelated to External linksEric0.60section
Petrie polygonrelated to External linksPetrie0.60section
Petrie polygonrelated to External linksMathWorld0.60section
Petrie polygonrelated to Further readingCoxeter0.60section
Petrie polygonrelated to Further readingRegular Polytopes0.60section
Petrie polygonrelated to Further readingNew York0.60section
Petrie polygonrelated to Further readingDover0.60section
Petrie polygonrelated to Further readingSec0.60section
Petrie polygonrelated to Further readingPetrie Polygons0.60section
Petrie polygonrelated to Further readingChapter0.60section
Petrie polygonrelated to Further readingThe0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Petrie polygon bring nearby vocabulary together. In this analysis, examples include Polygon, Polygons and Regular. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Petrie polygon
    • Polygon
    • Polygons
    • Regular
    • Skew
    • Polytopes
    • Also
    • One
    • Sides
    • Number
    • Plane
    • Coxeter
    • Dual
  • petrie polygon
    • Polygon
    • Polygons
    • Regular
    • Sides
    • Also
    • Skew
    • Polytopes
    • One
    • Number
    • Plane
    • Polychora
    • Polytope
  • skew polygon
    • Regular
    • Sides
    • Infinite
    • Three
    • Tilings
    • Polygons
    • Also
    • Skew
    • Polytopes
    • Number
    • Plane
    • Polychora
  • regular polytope
    • Polytopes
    • Skew
    • Plane
    • Polygons
    • Also
    • Polyhedra
    • Sides
    • Coxeter
    • Infinite
    • Polychora
    • Projected
    • Regular
  • regular polygon
    • Polytopes
    • Regular
    • Skew
    • Sides
    • Polygons
    • Also
    • Polyhedra
    • Coxeter
    • Number
    • Plane
    • Polychora
    • Polytope
  • regular polyhedron
    • Polytopes
    • Skew
    • Polygons
    • Also
    • Polyhedra
    • Sides
    • Coxeter
    • Infinite
    • Polychora
    • Projected
    • Three
    • Tilings
  • john flinders petrie
    • Flinders
    • John
    • Polygon
    • Polygons
    • Regular
    • Named
    • Polychora
    • Projections
    • Also
    • Polyhedra
    • Skew
    • Polytopes
  • petrie dual
    • Polygon
    • Polygons
    • Regular
    • Edges
    • Graph
    • Faces
    • Skew
    • Polytopes
    • Also
    • One
    • Surface
    • Sides

Connections between topic areas Semantic bridges

For Petrie polygon, one of the stronger structural bridges in this analysis connects Petrie polygon 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
Petrie polygon — Overview · splits 30 ⟂ 19
Petrie polygon — The Petrie polygons of the regular polyhedra · splits 35 ⟂ 14
Petrie polygon — History · splits 41 ⟂ 8
Petrie polygon — The Petrie polygon of regular polychora (4-polytopes) · splits 45 ⟂ 4
Petrie polygon — The Petrie polygon projections of regular and uniform polytopes · splits 46 ⟂ 3

Map overview Semantic statistics

Petrie polygon

Nodes49
Edges48
Triples41
Avg. degree1.96
Density0.040816
Components1

Source & methodology

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

Source: Wikipedia — Petrie polygon · EN edition · Analysis: TopicsToTalkAbout

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