Editing 600-cell (section)

{{Short description|Four-dimensional analog of the icosahedron}}
{{cleanup|reason=Excessive explanatory footnotes, some of which include other explanatory footnotes, which include other explanatory footnotes, and so on. Linearize by trimming for brevity, inserting into main text, or spawning subarticle(s). |date=March 2024}}
{{Infobox polychoron |
  Name=600-cell|
  Image_File=Schlegel_wireframe_600-cell_vertex-centered.png|
  Image_Caption=[[Schlegel diagram]], vertex-centered<br>(vertices and edges)|
  Type=[[Convex regular 4-polytope]]|
  Last=[[Rectified 600-cell|34]]|
  Index=35|
  Next=[[Truncated 120-cell|36]]|
  Schläfli={3,3,5}|
  CD={{CDD|node_1|3|node|3|node|5|node}}|
  Cell_List=600 ([[Tetrahedron|{3,3}]]) [[Image:Tetrahedron.png|20px]]|
  Face_List=1200 [[triangle|{3}]]|
  Edge_Count=720|
  Vertex_Count= 120|
  Petrie_Polygon=[[Triacontagon#Petrie polygons|30-gon]]|
  Coxeter_Group=H<sub>4</sub>, [3,3,5], order 14400|
  Vertex_Figure=[[Image:600-cell verf.svg|80px]]<br>[[icosahedron]]|
  Dual=[[120-cell]]|
  Property_List=[[Convex polytope|convex]], [[isogonal figure|isogonal]], [[isotoxal figure|isotoxal]], [[isohedral figure|isohedral]]
}}
[[File:600-cell net.png|thumb|right|[[Net (polyhedron)|Net]]]]
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 '''C<sub>600</sub>''', '''hexacosichoron'''<ref>[[Norman Johnson (mathematician)|N.W. Johnson]]: ''Geometries and Transformations'', (2018) {{ISBN|978-1-107-10340-5}} Chapter 11: ''Finite Symmetry Groups'', 11.5 ''Spherical Coxeter groups'', p.249</ref> and '''hexacosihedroid'''.<ref>Matila Ghyka, ''The Geometry of Art and Life'' (1977), p.68</ref>
It is also called a '''tetraplex''' (abbreviated from "tetrahedral complex") and a '''[[polytetrahedron]]''', being bounded by tetrahedral [[Cell (geometry)|cells]].

The 600-cell's boundary is composed of 600 [[Tetrahedron|tetrahedral]] [[Cell (mathematics)|cells]] with 20 meeting at each vertex.
Together they form 1200 triangular faces, 720 edges, and 120 vertices.
It is the 4-[[Four-dimensional space#Dimensional analogy|dimensional analogue]] of the [[icosahedron]], since it has five [[Tetrahedron|tetrahedra]] meeting at every edge, just as the icosahedron has five [[triangle]]s meeting at every vertex.
Its [[dual polytope]] is the [[120-cell]].