Grand 120-cell
regular star 4-polytope with Schläfli symbol {5,3,5/2}
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
It has the same edge arrangement as the 600-cell, icosahedral 120-cell and the same face arrangement as the great 120-cell.
It could be seen as another 4D analogue of the three-dimensional great dodecahedron due to being a pentagonal polytope with enlarged facets.
See also
List of regular polytopes
Convex regular 4-polytope
Kepler-Poinsot solids - regular star polyhedron
Star polygon - regular star polygons
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 [1].
H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.
The public source identifies “Grand 120-cell” as regular star 4-polytope with Schläfli symbol {5,3,5/2}. This brief keeps that definition visible, then builds a research path around Grand, 120-cell and regular.
Why this record matters
A short description can identify a subject without explaining its stakes. For “Grand 120-cell”, the useful work is to connect “regular star 4-polytope with Schläfli symbol {5,3,5/2}” to the records capable of establishing context and consequence.
The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated Sep 20, 2026. The linked authority identifier is Q5594220. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1883 and 1973.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Grand 120-cell”, its source revision and the description used here.
- Expand the search: follow Grand 120-cell primary sources, Grand 120-cell archive and Grand research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Grand 120-cell”?
- Which institution is responsible for the underlying evidence?
- What terminology or title could unlock a more precise catalogue search?
Search terms from this dossier
This entry incorporates text from “Grand 120-cell” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.