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600-cell: Symmetries, Overview & Geometry

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known as the C600, hexacosichoron, hexacosihedroid and hypericosahedron. It is also called a tetraplex (abbreviated from "tetrahedral complex") and a polytetrahedron, being bounded by tetrahedral cells.

Language: English [EN]
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600-cell topic overview

The analysis highlights Symmetries, Overview and Geometry as prominent areas in the source structure around 600-cell.

Related topics
124
Source areas
6
Connected nodes
130
Extracted relationships
63
Concept neighborhoods
19
Bridge connections
130

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 · 92 topics
Symmetries · 17 topics
Geometry · 5 topics
Related polytopes and honeycombs · 4 topics
Diminished 600-cells · 3 topics
Visualization · 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.

Key facts & relationships

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

Cells
600 ({3,3})
Coxeter group
H4, [3,3,5], order 14400
Dual
120-cell
Edges
720
Faces
1200 {3}
Petrie polygon
30-gon

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

Geometry

Symmetries

Visualization

Diminished 600-cells

Related polytopes and honeycombs

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 600-cell connects Entity context

The extracted context around 600-cell shows recurring relationship patterns in the source. For example, 600-cell → Cell, Cell Vertex, Der, Eric, German, Klitzing, Marco Möller's Regular, MathWorld, R4, Richard, The, Weisstein, Zeller Another extracted example is 600-cell → Cartesian, Each, Euclidean, Hamiltonian, Id, It, Mebius, RSG, The, This, We, When. Use these groups to spot repeated connection types before inspecting the individual relationships.

600-cell

Top relations

related to External links · 13
600-cell → Cell, Cell Vertex, Der, Eric, German, Klitzing, Marco Möller's Regular, MathWorld, R4, Richard, The, Weisstein, Zeller
related to Symmetries · 12
600-cell → Cartesian, Each, Euclidean, Hamiltonian, Id, It, Mebius, RSG, The, This, We, When
is a · 5
600-cell → convex regular 4-polytope, Coxeter group H4, dual of the 120-cell, fifth in the sequence of 6 convex regular 4-polytopes in order of complexity, icosahedron.Twenty tetrahedral cells meet at each vertex
related to Related polytopes and honeycombs · 5
600-cell → All, Euclidean, H4, It, The
related to 3D projections · 3
600-cell → Institut Henri Poincaré, Man Ray, Shakesperean Equation
related to Rotations · 3
600-cell → Euclidean, SO, The
related to As a configuration · 2
600-cell → The, This
related to Constructions · 2
600-cell → Consequently, The
related to Diminished 600-cells · 2
600-cell → The, This
related to Geometry · 2
600-cell → It, The

Important terminology

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

Important terminology

vertices great 24-cell parallel rotation edges displaystyle cells tetrahedral citation needed decagons two clifford isoclinic vertex sqrt 24-cells one cell

600-cell relationships Subject–Predicate–Object triples

TTTA extracted 63 structured relationships around 600-cell. Examples in this analysis include 600-cell → Cells → 600 ({3,3}) and 600-cell → Coxeter group → H4, [3,3,5], order 14400. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
600-cellCells600 ({3,3})1.00infobox
600-cellCoxeter groupH4, [3,3,5], order 144001.00infobox
600-cellDual120-cell1.00infobox
600-cellEdges7201.00infobox
600-cellFaces1200 {3}1.00infobox
600-cellPetrie polygon30-gon1.00infobox
600-cellPropertiesconvex, isogonal, isotoxal, isohedral1.00infobox
600-cellSchläfli symbol{3,3,5}1.00infobox
600-cellTypeConvex regular 4-polytope1.00infobox
600-cellUniform index351.00infobox
600-cellVertex figureicosahedron1.00infobox
600-cellVertices1201.00infobox
600-cellis aconvex regular 4-polytope0.90text
600-cellis afifth in the sequence of 6 convex regular 4-polytopes in order of complexity0.90text
600-cellis aicosahedron.Twenty tetrahedral cells meet at each vertex0.90text
600-cellis aCoxeter group H40.90text
600-cellis adual of the 120-cell0.90text

Related concept clusters Concept neighborhoods

The concept neighborhoods around 600-cell bring nearby vocabulary together. In this analysis, examples include Vertices, Citation and Needed. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • 600-cell
    • Vertices
    • Citation
    • Needed
    • Great
    • 24-cell
    • Cells
    • Displaystyle
    • Edges
    • Tetrahedral
    • Isoclinic
    • Vertex
    • Cell
  • 600-cell
    • Vertices
    • Citation
    • Needed
    • Great
    • 24-cell
    • Cells
    • Displaystyle
    • Edges
    • Tetrahedral
    • Isoclinic
    • Vertex
    • Cell
  • cells
    • Tetrahedral
    • Citation
    • Needed
    • Rings
    • 600-cell
    • Cell
    • Vertices
    • 24-cell
    • Edges
    • Displaystyle
    • Isoclines
    • Fibration
  • 16-cell's rotation of just 2 invariant great square planes
    • Left
    • Right
    • Rotation
    • Isoclinic
    • Parallel
    • Vertices
    • Clifford
    • Citation
    • Needed
    • Squares
    • Hexagons
    • Isocline
  • 24-cell's rotation in 6 clifford parallel great squares
    • Parallel
    • Left
    • Right
    • Vertices
    • Clifford
    • Great
    • Disjoint
    • Citation
    • Needed
    • Isoclinic
    • Squares
    • Fibration
  • snub 24-cell
    • 600-cell
    • Vertices
    • Citation
    • Needed
    • Displaystyle
    • Cells
    • Tetrahedral
    • Sqrt
    • Isoclinic
    • Two
    • 24-cells
    • Phi
  • fibrations of its 450 great squares
    • Parallel
    • Vertices
    • Rings
    • Clifford
    • Citation
    • Needed
    • Squares
    • Hexagons
    • Great
    • Planes
    • One
    • Fibration
  • great circle
    • Parallel
    • Vertices
    • Clifford
    • Citation
    • Needed
    • Squares
    • Hexagons
    • Planes
    • Fibration
    • Decagon
    • Rotation
    • Isoclinic

Connections between topic areas Semantic bridges

For 600-cell, one of the stronger structural bridges in this analysis connects 600-cell 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
600-cell — Overview · splits 38 ⟂ 93
600-cell — Symmetries · splits 113 ⟂ 18
600-cell — Geometry · splits 125 ⟂ 6
600-cell — Related polytopes and honeycombs · splits 126 ⟂ 5
600-cell — Visualization · splits 127 ⟂ 4
600-cell — Diminished 600-cells · splits 127 ⟂ 4

Map overview Semantic statistics

600-cell

Nodes131
Edges130
Triples63
Avg. degree1.98
Density0.015267
Components1

Source & methodology

TTTA analyzes the structure around 600-cell to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Symmetries, Overview & Geometry, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — 600-cell · EN edition · Analysis: TopicsToTalkAbout

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