Vertex figure
figure exposed when a corner of a polyhedron or polytope is sliced off
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a general n-polytope is sliced off.
Definitions
Take some corner or vertex of a polyhedron. Mark a point somewhere along each connected edge. Draw lines across the connected faces, joining adjacent points around the face. When done, these lines form a complete circuit, i.e. a polygon, around the vertex. This polygon is the vertex figure.
More precise formal definitions can vary quite widely, according to circumstance. For example Coxeter (e.g. 1948, 1954) varies his definition as convenient for the current area of discussion.
The public source identifies “Vertex figure” as figure exposed when a corner of a polyhedron or polytope is sliced off. This brief keeps that definition visible, then builds a research path around Vertex, figure and exposed.
Why this record matters
A short description can identify a subject without explaining its stakes. For “Vertex figure”, the useful work is to connect “figure exposed when a corner of a polyhedron or polytope is sliced off” to the records capable of establishing context and consequence.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Jun 29, 2026. The linked authority identifier is Q598843. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1948 and 1954.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. 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 “Vertex figure”, its source revision and the description used here.
- Expand the search: follow Vertex figure primary sources, Vertex figure archive and Vertex 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 “Vertex figure”?
- Which cited source is closest to the event, object or claim?
- Which institution is responsible for the underlying evidence?
Search terms from this dossier
This entry incorporates text from “Vertex figure” 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.