View source for Great grand 120-cell

{| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Great grand 120-cell
|-
|bgcolor=#ffffff align=center colspan=2|[[Image:Ortho solid 011-uniform polychoron 53p-t0.png|280px]]<BR>Orthogonal projection
|-
|bgcolor=#e7dcc3|Type||Schläfli-Hess polytope
|-
|bgcolor=#e7dcc3|Cells||120 [[Great dodecahedron|{5,5/2}]]
|-
|bgcolor=#e7dcc3|Faces||720 [[Pentagon|{5}]]
|-
|bgcolor=#e7dcc3|Edges||1200
|-
|bgcolor=#e7dcc3|Vertices||120
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[Great stellated dodecahedron|{5/2,3}]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]|| {5,5/2,3}
|-
|bgcolor=#e7dcc3|Coxeter-Dynkin diagram||{{CDD|node_1|5|node|5|rat|d2|node|3|node}}
|-
|bgcolor=#e7dcc3|[[Coxeter group|Symmetry group]]||H<sub>4</sub>, [3,3,5]
|-
|bgcolor=#e7dcc3|Dual|| [[Great icosahedral 120-cell]]
|-
|bgcolor=#e7dcc3|Properties|| Regular
|}
In [[Geometry|geometry]], the '''great grand 120-cell''' or '''great grand polydodecahedron''' is a regular star 4-polytope with [[Schläfli symbol]] {5,5/2,3}. It is one of 10 regular Schläfli-Hess polytopes.

== Related polytopes ==

It has the same edge arrangement as the [[Small stellated 120-cell|small stellated 120-cell]].

{| class="wikitable" width=600
|+ [[Orthographic projection]]s by Coxeter planes
|- align=center
!H<sub>3</sub>
!A<sub>2</sub> / B<sub>3</sub> / D<sub>4</sub>
!A<sub>3</sub> / B<sub>2</sub>
|- align=center
|[[File:Small stellated 120-cell ortho-10gon.png|200px]]
|[[File:Small stellated 120-cell ortho-6gon.png|200px]]
|[[File:Small stellated 120-cell ortho-4gon.png|200px]]
|}

== See also ==
* List of regular polytopes
* Convex regular 4-polytope
* Kepler-Poinsot polyhedron – regular [[Star polyhedron|star polyhedron]]
* [[Star polygon]] – regular star polygons

== External links ==
* [http://hometown.aol.com/hedrondude/regulars.html Regular polychora] {{Webarchive|url=https://web.archive.org/web/20030906012615/http://hometown.aol.com/hedrondude/regulars.html |date=2003-09-06 }}
* [http://mathforum.org/library/drmath/view/54786.html Discussion on names]
* [https://web.archive.org/web/20061107052613/http://www.mathematik.uni-regensburg.de/Goette/sterne/ Reguläre Polytope]
* [https://web.archive.org/web/20070704012333/http://davidf.faricy.net/polyhedra/Star_Polychora.html The Regular Star Polychora]

== References ==
* Edmund Hess, (1883) ''Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder'' [http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=ABN8623.0001.001].
*H. S. M. Coxeter, ''Regular Polytopes'', 3rd. ed., Dover Publications, 1973. {{ISBN|0-486-61480-8}}.
* [[Biography:John Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-Strauss, ''The Symmetries of Things'' 2008, {{ISBN|978-1-56881-220-5}} (Chapter 26, Regular Star-polytopes, pp.&nbsp;404–408)
* {{KlitzingPolytopes|polychora.htm|4D uniform polytopes (polychora)|o3o5/2o5x - gaghi}}
{{Regular 4-polytopes}}
[[Category:4-polytopes]]

{{Sourceattribution|Great grand 120-cell}}