600-cell

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Export map as:

Research this topic

Explore the main themes, entities and connections around 600-cell. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Symmetries

Quaternions Golden field Rational numbers Four-dimensional Euclidean geometry Group

17 related topics

Overview

Geometry Convex regular 4-polytope Platonic solid Schläfli symbol Polytetrahedron

92 related topics

Geometry

Expression Symmetry SO(4)Group Configuration matrix

5 related topics

Related polytopes and honeycombs

Order-6 tetrahedral honeycomb Hyperbolic space Regular complex polygons Complex reflection group

4 related topics

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

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Geometry
Convex regular 4-polytope
Platonic solid
Schläfli symbol
Polytetrahedron
Cells Cell (geometry)
Characteristic tetrahedron of the regular tetrahedron Tetrahedron
Cells Cell (mathematics)
Dimensional analogue Four-dimensional space
Icosahedron
Triangles Triangle
Dual polytope
120-cell
Even permutations Even permutation
16-cell's rotation of just 2 invariant great square planes 16-cell
Radially equilateral Tesseract
24-cell's rotation in 6 Clifford parallel great squares 24-cell
Snub 24-cell
Fibrations of its 450 great squares 600-cell
Icosians Icosian
Orthonormal basis
Geometric configuration Configuration (geometry)
Pentagons Pentagon
Decagram {10/3} Decagon
Completely orthogonal
Isoclinic rotation Rotations in 4-dimensional Euclidean space
Hypersphere
Dodecahedron
Icosidodecahedron
Coxeter plane

Geometry

Expression Group action
Symmetry Symmetry (geometry)
SO(4)
Group Orthogonal group
Configuration matrix Regular 4-polytope

Symmetries

Quaternions Quaternion
Golden field
Rational numbers Rational number
Four-dimensional Euclidean geometry Euclidean geometry
Group Group (mathematics)
Binary icosahedral group
Icosahedral group
Rotational symmetry
Invariant subgroup
Centre Center of a group
Quaternion algebra
Isomorphic
SL(2,5) Special linear group
Symmetry group
Coxeter group H4 H4 (mathematics)
Rotations Rotation (mathematics)
Clifford algebra

Visualization

Diminished 600-cells

Related polytopes and honeycombs

Order-6 tetrahedral honeycomb
Hyperbolic space
Regular complex polygons Regular complex polytope
Complex reflection group

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.

Map overview Semantic statistics

Nodes131

Edges130

Triples63

Avg. degree1.98

Density0.015267

Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

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 Word statistics

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

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
600-cell	Cells	600 ({3,3})	1.00	infobox
600-cell	Coxeter group	H4, [3,3,5], order 14400	1.00	infobox
600-cell	Dual	120-cell	1.00	infobox
600-cell	Edges	720	1.00	infobox
600-cell	Faces	1200 {3}	1.00	infobox
600-cell	Petrie polygon	30-gon	1.00	infobox
600-cell	Properties	convex, isogonal, isotoxal, isohedral	1.00	infobox
600-cell	Schläfli symbol	{3,3,5}	1.00	infobox
600-cell	Type	Convex regular 4-polytope	1.00	infobox
600-cell	Uniform index	35	1.00	infobox
600-cell	Vertex figure	icosahedron	1.00	infobox
600-cell	Vertices	120	1.00	infobox
600-cell	is a	convex regular 4-polytope	0.90	text
600-cell	is a	fifth in the sequence of 6 convex regular 4-polytopes in order of complexity	0.90	text
600-cell	is a	icosahedron.Twenty tetrahedral cells meet at each vertex	0.90	text
600-cell	is a	Coxeter group H4	0.90	text
600-cell	is a	dual of the 120-cell	0.90	text

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

Connections between topic areas Semantic bridges

Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

Min side: 3