Editing 120-cell (section)

{{Short description|Four-dimensional analog of the dodecahedron}}
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{{Infobox polychoron
|  Name=120-cell
|  Image_File=Schlegel wireframe 120-cell.png
|  Image_Caption=[[Schlegel diagram]]<br>(vertices and edges)
|  Type=[[Convex regular 4-polytope]]
|  Last=[[Snub 24-cell|31]]
|  Index=32
|  Next=[[Rectified 120-cell|33]]
|  Schläfli={5,3,3}|
  CD={{CDD|node_1|5|node|3|node|3|node}}|
  Cell_List=120 [[Dodecahedron|{5,3}]] [[Image:Dodecahedron.png|20px]]|
  Face_List=720 [[pentagon|{5}]] [[File:Regular pentagon.svg|20px]]|
  Edge_Count=1200|
  Vertex_Count= 600|
  Petrie_Polygon=[[triacontagon|30-gon]]|
  Coxeter_Group=H<sub>4</sub>, [3,3,5]|
  Vertex_Figure=[[File:120-cell verf.svg|80px]]<br>[[tetrahedron]]|
  Dual=[[600-cell]]|
  Property_List=[[convex set|convex]], [[isogonal figure|isogonal]], [[isotoxal figure|isotoxal]], [[isohedral figure|isohedral]]
}}
[[File:120-cell net.png|thumb|right|[[Net (polyhedron)|Net]]]]
In [[geometry]], the '''120-cell''' is the [[convex regular 4-polytope]] (four-dimensional analogue of a [[Platonic solid]]) with [[Schläfli symbol]] {5,3,3}. It is also called a '''C<sub>120</sub>''',  '''dodecaplex''' (short for "dodecahedral complex"), '''hyperdodecahedron''', '''polydodecahedron''', '''hecatonicosachoron''', '''dodecacontachoron'''<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 '''hecatonicosahedroid'''.<ref>Matila Ghyka, ''The Geometry of Art and Life'' (1977), p.68</ref>

The boundary of the 120-cell is composed of 120 dodecahedral [[cell (mathematics)|cells]] with 4 meeting at each vertex. Together they form 720 [[pentagon]]al faces, 1200 edges, and 600 vertices. It is the 4-[[Four-dimensional space#Dimensional analogy|dimensional analogue]] of the [[regular dodecahedron]], since just as a dodecahedron has 12 pentagonal facets, with 3 around each vertex, the ''dodecaplex'' has 120 dodecahedral facets, with 3 around each edge.{{Efn|In the 120-cell, 3 dodecahedra and 3 pentagons meet at every edge. 4 dodecahedra, 6 pentagons, and 4 edges meet at every vertex. The dihedral angle (between dodecahedral hyperplanes) is 144°.{{Sfn|Coxeter|1973|loc=Table I(ii); "120-cell"|pp=292-293}}|name=dihedral}} Its dual polytope is the [[600-cell]].