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Regular polytope: History & Art
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves…
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Regular polytope topic overview
The analysis highlights History and Art as prominent areas in the source structure around Regular polytope.
Related topics
159
Source areas
5
Connected nodes
178
Extracted relationships
179
Concept neighborhoods
55
Bridge connections
178
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.
Description · 49 topics
History of discovery · 38 topics
Overview · 30 topics
Classifications · 24 topics
Constructions · 18 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.
Explore all related topics Closing gaps
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.
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.
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
How Regular polytope connects Entity context
Entity context groups extracted connections by relationship type. Counts show recurrence in the analyzed source; the examples are research signals, not claims about importance.
The extracted context around Regular polytope shows recurring relationship patterns in the source. For example, Regular polytope → Abstract Regular Polytopes, American Journal, Applied Mathematics, Arnold, Artmann, Augustin-Louis, Barnes, Benno, Cambridge University Press, Cauchy, Colloquium Internationale CNRS, Complexes, Concepts, Courier Dover, Coxeter, Cromwell, Crystallography, David, Deloudi, Denkschriften Another extracted example is Regular polytope → Alicia Boole Stott, Between, CITEREFSchläfli1858, Coxeter, English, Five, His, It, Ludwig Schläfli, Platonic, Reinhold Hoppe, Schläfli, Schläfli's, Swiss, The. Use these groups to spot repeated connection types before inspecting the individual relationships.
Regular polytope → Alicia Boole Stott, Between, CITEREFSchläfli1858, Coxeter, English, Five, His, It, Ludwig Schläfli, Platonic, Reinhold Hoppe, Schläfli, Schläfli's, Swiss, The
related to Apeirotopes — infinite polytopes· 11
Regular polytope → Branko Grünbaum, Coxeter, He, In, It, More, Nowadays, Petrie, Since, The, They
related to Star polygons and polyhedra· 11
Regular polytope → Augustin Cauchy, Bradwardinus, Euclid, Johannes Kepler, Kepler-Poinsot, Louis Poinsot, Renaissance, The, These, Thomas Bradwardine, Various
related to Classification by Coxeter groups· 6
Regular polytope → Coxeter, Coxeter-Dynkin, Regular, Reversing, The, These
related to Schläfli symbols· 5
Regular polytope → Ludwig Schläfli, Platonic, So, The, This
related to Description· 4
Regular polytope → In, Regular, The, There
related to Duality of the regular polytopes· 3
Regular polytope → For, The, The Schläfli
related to External links· 3
Regular polytope → List, Small Regular Polytopes, The Atlas
see also· 3
Regular polytope → Leendert, List, Waerden
Important terminology
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.
Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Relationships are represented as Subject → Predicate → Object triples. Confidence describes extraction strength, not the real-world importance of a relationship; lower-confidence rows may be contextual rather than explicit.
TTTA extracted 179 structured relationships around Regular polytope. Examples in this analysis include Regular polytope → is a → polytope whose symmetry group acts transitively on its flags and Regular polytope → is a → dual of the dual polytope's facet. The table shows each extracted connection, where it came from and its confidence.
Subject
Predicate
Object
Confidence
Src
Regular polytope
is a
polytope whose symmetry group acts transitively on its flags
0.90
text
Regular polytope
is a
dual of the dual polytope's facet
0.90
text
Arthur Cayley
instance of
mathematicians
0.80
text
Ludwig Schläfli had developed the theory of regular polytopes in four
instance of
mathematicians
0.80
text
higher dimensions
instance of
mathematicians
0.80
text
such as the tesseract
instance of
mathematicians
0.80
text
the 24-cell.The latter are difficult
instance of
mathematicians
0.80
text
the 57-cell or the 11-cell
instance of
can be directly visualised and depicted using 4-dimensional stereographs.Harder still to imagine are the more modern abstract regular polytopes
0.80
text
the one shown can already give some limited insight into the structure of the polytope.Another way a three-dimensional viewer can comprehend the structure of a four-dimensional polytope is through being
instance of
even a simple animation
0.80
text
Regular polytope
related to Apeirotopes — infinite polytopes
In
0.60
section
Regular polytope
related to Apeirotopes — infinite polytopes
Coxeter
0.60
section
Regular polytope
related to Apeirotopes — infinite polytopes
Petrie
0.60
section
No triples extracted yet.
Related concept clusters Concept neighborhoods
Concept neighborhoods group terms that sit near one another in the extracted graph. They are useful for discovering adjacent language and context, but proximity does not by itself imply a factual relationship.
The concept neighborhoods around Regular polytope bring nearby vocabulary together. In this analysis, examples include Polytopes, Regular and Symmetry. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
Regular polytope
Polytopes
Regular
Symmetry
Polygons
Dimensions
Abstract
Vertex
Polyhedra
Dual
Displaystyle
Groups
Example
regular polytope
Polytopes
Regular
Vertex
Abstract
Symmetry
Polygons
Dimensions
Whose
May
Polyhedra
Dual
Figures
polytope
Regular
Vertex
Abstract
Whose
May
Symmetry
Dual
Figures
Faces
Elements
Also
Dimension
symmetry group
Symmetry
Groups
Displaystyle
Coxeter
Polytope
Example
Polytopes
Simplex
Whose
One
Vertex
Also
regular polygons
Polytopes
Symmetry
Polyhedra
Polygons
Regular
Dimensions
Abstract
Vertex
Example
Displaystyle
Figures
Groups
regular polyhedra
Polytopes
Symmetry
Polygons
Dimensions
Abstract
Vertex
Polyhedra
Regular
Dodecahedron
Displaystyle
Groups
Cube
abstract polytope
Polytopes
Regular
Vertex
Abstract
Polytope
Faces
Figure
Whose
Example
May
Elements
Symmetry
one dimension
Elements
Simplex
Space
Also
Symmetry
Whose
Displaystyle
Polyhedron
Two
Edges
One
Polytope
Connections between topic areas Semantic bridges
Semantic bridges connect parts of the graph that would otherwise be more separate. A bridge is a structural signal in this analysis, not a claim that the two topic areas are equivalent.
For Regular polytope, one of the stronger structural bridges in this analysis connects Regular polytope with Description. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.
Regular polytope
Nodes179
Edges178
Triples179
Avg. degree1.99
Density0.011173
Components1
Source & methodology
TTTA analyzes the structure around Regular polytope to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History & Art, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
