Regular polygon

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Regular polygon topic overview

The analysis highlights Regular convex polygons, General properties and Regular star polygons as prominent areas in the source structure around Regular polygon.

Related topics: 88
Source areas: 8
Connected nodes: 96
Extracted relationships: 71
Concept neighborhoods: 41
Bridge connections: 96

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.

Regular convex polygons · 23 topics

General properties · 15 topics

Overview · 14 topics

Regular star polygons · 13 topics

Constructible polygon · 11 topics

Regular polygons as faces of polyhedra · 7 topics

Regular skew polygons · 4 topics

Duality of regular polygons · 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.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Area (with side length s {\displaystyle s} ): A = 1 4 n s 2 cot ⁡ ( π n ) {\displaystyle A={\tfrac {1}{4}}ns^{2}\cot \left({\frac {\pi }{n}}\right)}
Circumscribed circle diameter: d OC = s csc ⁡ ( π n ) {\displaystyle d_{\text{OC}}=s\csc \left({\frac {\pi }{n}}\right)}
Dual polygon: Self-dual
Edges and vertices: n {\displaystyle n}
Inscribed circle diameter: d IC = s cot ⁡ ( π n ) {\displaystyle d_{\text{IC}}=s\cot \left({\frac {\pi }{n}}\right)}
Internal angle: ( n − 2 ) × π n {\displaystyle (n-2)\times {\frac {\pi }{n}}}

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

Euclidean geometry
Polygon
Direct equiangular Equiangular polygon
Equilateral Equilateral polygon
Convex Convex polygon
Star Star polygon
Limit Limit (mathematics)
Circle
Perimeter
Area
Apeirogon
Straight line Line (geometry)
Apothem
Viviani's theorem

General properties

Regular convex polygons

Simple polygons Simple polygon
Similar Similarity (geometry)
Schläfli symbol
Degenerate Degeneracy (mathematics)
Monogon
Abstract polygon Abstract polytope
Digon
Uniform polyhedra
Interior angle
Turns Turn (geometry)
Exterior angle
Supplementary Supplementary angle
Myriagon
Diagonals Diagonal
Circumradius
Constructible polygons Constructible polygon
Algebraic expressions Algebraic expression
Coxeter
Zonogon
M-cubes Hypercube
OEIS On-Line Encyclopedia of Integer Sequences
Side Edge (geometry)
Since cot ⁡ x → 1 / x {\displaystyle \cot x\rightarrow 1/x} as x → 0 {\displaystyle x\rightarrow 0} Trigonometric functions

Constructible polygon

Construct with compass and straightedge Compass-and-straightedge construction
Ancient Greek mathematicians Greek mathematics
Carl Friedrich Gauss
17-gon Heptadecagon
Gaussian periods Gaussian period
Disquisitiones Arithmeticae
Sufficient condition
Necessary Necessary condition
Pierre Wantzel
Cosine
Constructible number

Regular skew polygons

Duality of regular polygons

Congruency Congruency (geometry)

Regular polygons as faces of polyhedra

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 Regular polygon connects Entity context

The extracted context around Regular polygon shows recurring relationship patterns in the source. For example, Regular polygon → Archived, Convergence Archived, Eric, MathWorld, Regular, Regular Polygon Three, Regular Polygon With, Wayback Machine, Weisstein, With Another extracted example is Regular polygon → Carl Friedrich Gauss, Disquisitiones Arithmeticae, Five, Gaussian, Greek, If, Some, The, This. Use these groups to spot repeated connection types before inspecting the individual relationships.

Top relations

related to External links · 10

Regular polygon → Archived, Convergence Archived, Eric, MathWorld, Regular, Regular Polygon Three, Regular Polygon With, Wayback Machine, Weisstein, With

related to Constructible polygon · 9

Regular polygon → Carl Friedrich Gauss, Disquisitiones Arithmeticae, Five, Gaussian, Greek, If, Some, The, This

related to Symmetry · 8

Regular polygon → Cn, D2, D3, D4, Dn, If, It, The

related to Dissections · 7

Regular polygon → A006245, Coxeter, In, OEIS, Regular, The, These

is a · 5

Regular polygon → cyclic polygon.Together with the property of equal-length sides, dihedral group Dn, polygon that is direct equiangular, regular star polygon, tangential polygon.A regular n-sided polygon can be constructed with compass and straightedge if and only if the odd prime factors of n are distinct Fermat primes. .mw-parser-ou…

related to Regular convex polygons · 5

Regular polygon → All, An, For, Schläfli, Those

related to Regular skew polygons · 4

Regular polygon → All, Examples, More, Petrie

related to Regular star polygons · 4

Regular polygon → For, If, Schläfli, The

related to Area · 3

Regular polygon → For, Since, The

related to Circumradius · 2

Regular polygon → For, The

Important terminology

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

Important terminology

regular polygon polygons sides convex vertices displaystyle number circle circumradius star length side point angle two n-gon coxeter also area

Regular polygon relationships Subject–Predicate–Object triples

TTTA extracted 71 structured relationships around Regular polygon. Examples in this analysis include Regular polygon → Area (with side length s {\displaystyle s} ) → A = 1 4 n s 2 cot ⁡ ( π n ) {\displaystyle A={\tfrac {1}{4}}ns^{2}\cot \left({\frac {\pi }{n}}\right)} and Regular polygon → Circumscribed circle diameter → d OC = s csc ⁡ ( π n ) {\displaystyle d_{\text{OC}}=s\csc \left({\frac {\pi }{n}}\right)}. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Regular polygon	Area (with side length s {\displaystyle s} )	A = 1 4 n s 2 cot ⁡ ( π n ) {\displaystyle A={\tfrac {1}{4}}ns^{2}\cot \left({\frac {\pi }{n}}\right)}	1.00	infobox
Regular polygon	Circumscribed circle diameter	d OC = s csc ⁡ ( π n ) {\displaystyle d_{\text{OC}}=s\csc \left({\frac {\pi }{n}}\right)}	1.00	infobox
Regular polygon	Dual polygon	Self-dual	1.00	infobox
Regular polygon	Edges and vertices	n {\displaystyle n}	1.00	infobox
Regular polygon	Inscribed circle diameter	d IC = s cot ⁡ ( π n ) {\displaystyle d_{\text{IC}}=s\cot \left({\frac {\pi }{n}}\right)}	1.00	infobox
Regular polygon	Internal angle	( n − 2 ) × π n {\displaystyle (n-2)\times {\frac {\pi }{n}}}	1.00	infobox
Regular polygon	Internal angle sum	( n − 2 ) × π {\displaystyle \left(n-2\right)\times {\pi }}	1.00	infobox
Regular polygon	Properties	Convex, cyclic, equilateral, isogonal, isotoxal	1.00	infobox
Regular polygon	Schläfli symbol	{ n } {\displaystyle \{n\}}	1.00	infobox
Regular polygon	Symmetry group	Dn, order 2n	1.00	infobox
Regular polygon	is a	polygon that is direct equiangular	0.90	text
Regular polygon	is a	cyclic polygon.Together with the property of equal-length sides	0.90	text
Regular polygon	is a	tangential polygon.A regular n-sided polygon can be constructed with compass and straightedge if and only if the odd prime factors of n are distinct Fermat primes. .mw-parser-ou…	0.90	text
Regular polygon	is a	dihedral group Dn	0.90	text
Regular polygon	is a	regular star polygon	0.90	text

Related concept clusters Concept neighborhoods

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

Regular polygon
- Regular
- Polygons
- Sides
- Displaystyle
- Convex
- Vertices
- Circumradius
- N-gon
- Distances
- One
- Sum
- Length
regular polygon
- Regular
- Polygons
- Circle
- Sides
- N-sided
- Displaystyle
- Convex
- Side
- Vertices
- Circumradius
- N-gon
- One
polygon
- Regular
- Circle
- Sides
- N-sided
- Polygons
- Side
- Convex
- One
- Length
- Circumradius
- Number
- Displaystyle
equilateral
- Length
- Circle
- Convex
- Area
- Pentagon
- Polyhedra
- Schläfli
- Skew
- Symmetry
- Constructible
- Edges
- Coxeter
convex
- N-sided
- One
- Displaystyle
- Equilateral
- Polygons
- Area
- Polyhedra
- Schläfli
- Regular
- Coxeter
- Faces
- Star
circle
- Polygon
- Equilateral
- Sides
- Number
- Area
- Vertices
- Internal
- Also
- Length
- Side
- Angle
- Convex
area
- N-sided
- Length
- Side
- Circumradius
- Polygons
- Circle
- Convex
- Equilateral
- Displaystyle
- Line
- Pentagon
- Polyhedra
circumscribed circle
- Polygon
- Equilateral
- Sides
- Number
- Area
- Vertices
- Internal
- Also
- Length
- Side
- Angle
- Convex

Connections between topic areas Semantic bridges

For Regular polygon, one of the stronger structural bridges in this analysis connects Regular polygon with 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

Regular polygon — Regular convex polygons · splits 73 ⟂ 24

Regular polygon — General properties · splits 81 ⟂ 16

Regular polygon — Overview · splits 82 ⟂ 15

Regular polygon — Regular star polygons · splits 83 ⟂ 14

Regular polygon — Constructible polygon · splits 85 ⟂ 12

Regular polygon — Regular polygons as faces of polyhedra · splits 89 ⟂ 8

Regular polygon — Regular skew polygons · splits 92 ⟂ 5

Map overview Semantic statistics

Regular polygon

Nodes97

Edges96

Triples71

Avg. degree1.98

Density0.020619

Components1

Source & methodology

TTTA analyzes the structure around Regular polygon to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Regular convex polygons, General properties & Regular 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 — Regular polygon · EN edition · Analysis: TopicsToTalkAbout