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Grand 120-cell

October 21, 2023

Grand 120-cell

Orthogonal projection
Type Schläfli-Hess polytope
Cells 120 {5,3}
Faces 720 {5}
Edges 720
Vertices 120
Vertex figure {3,5/2}
Schläfli symbol {5,3,5/2}
Coxeter-Dynkin diagram
Symmetry group H4, [3,3,5]
Dual Great stellated 120-cell
Properties Regular

In geometry, the grand 120-cell or grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes.

It is one of four regular star 4-polytopes discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids.

Related polytopes Edit

It has the same edge arrangement as the 600-cell, icosahedral 120-cell and the same face arrangement as the great 120-cell.

Orthographic projections by Coxeter planes
H4 - F4
 
[30] 		 
[20] 		 
[12]
H3 A2 / B3 / D4 A3 / B2
 
[10] 		 
[6] 		 
[4]

See also Edit

References Edit

  • Edmund Hess, (1883) Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder [1].
  • H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26, Regular Star-polytopes, pp. 404–408)
  • Klitzing, Richard. "4D uniform polytopes (polychora) o5o3o5/2x - gahi".

External links Edit

 

This 4-polytope article is a stub. You can help Wikipedia by expanding it.

October 21, 2023
grand, cell, orthogonal, projectiontype, schläfli, hess, polytopecells, faces, edges, 720vertices, 120vertex, figure, schläfli, symbol, coxeter, dynkin, diagramsymmetry, group, dual, great, stellated, cellproperties, regularin, geometry, grand, cell, grand, po. Grand 120 cellOrthogonal projectionType Schlafli Hess polytopeCells 120 5 3 Faces 720 5 Edges 720Vertices 120Vertex figure 3 5 2 Schlafli symbol 5 3 5 2 Coxeter Dynkin diagramSymmetry group H4 3 3 5 Dual Great stellated 120 cellProperties RegularIn geometry the grand 120 cell or grand polydodecahedron is a regular star 4 polytope with Schlafli symbol 5 3 5 2 It is one of 10 regular Schlafli Hess polytopes It is one of four regular star 4 polytopes discovered by Ludwig Schlafli It is named by John Horton Conway extending the naming system by Arthur Cayley for the Kepler Poinsot solids Contents 1 Related polytopes 2 See also 3 References 4 External linksRelated polytopes EditIt has the same edge arrangement as the 600 cell icosahedral 120 cell and the same face arrangement as the great 120 cell Orthographic projections by Coxeter planes H4 F4 nbsp 30 nbsp 20 nbsp 12 H3 A2 B3 D4 A3 B2 nbsp 10 nbsp 6 nbsp 4 See also EditList of regular polytopes Convex regular 4 polytope Kepler Poinsot solids regular star polyhedron Star polygon regular star polygonsReferences EditEdmund Hess 1883 Einleitung in die Lehre von der Kugelteilung mit besonderer Berucksichtigung ihrer Anwendung auf die Theorie der Gleichflachigen und der gleicheckigen Polyeder 1 H S M Coxeter Regular Polytopes 3rd ed Dover Publications 1973 ISBN 0 486 61480 8 John H Conway Heidi Burgiel Chaim Goodman Strass The Symmetries of Things 2008 ISBN 978 1 56881 220 5 Chapter 26 Regular Star polytopes pp 404 408 Klitzing Richard 4D uniform polytopes polychora o5o3o5 2x gahi External links EditRegular polychora Archived 2003 09 06 at the Wayback Machine Discussion on names Regulare Polytope The Regular Star Polychora nbsp This 4 polytope article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Grand 120 cell amp oldid 1131066471, wikipedia, wiki, book, books, library,

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