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Regular polygonal complexes in space, I

2010· article· en· W4245170112 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueTransactions of the American Mathematical Society · 2010
Typearticle
Languageen
FieldComputer Science
TopicComputational Geometry and Mesh Generation
Canadian institutionsYork University
Fundersnot available
KeywordsMathematicsCombinatoricsFlag (linear algebra)Vertex (graph theory)Transitive relationAlgebraic numberFLAGS registerEuclidean spaceEuclidean geometrySuccessor cardinalVector spaceGroup (periodic table)Discrete mathematicsPure mathematicsAlgebra over a fieldGeometryGraphComputer science

Abstract

fetched live from OpenAlex

A polygonal complex in Euclidean $3$-space $\mathbb {E}^3$ is a discrete poly- hedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number $r\geqslant 2$ of faces surround each edge. It is said to be regular if its symmetry group is transitive on the flags. The present paper and its successor describe a complete classification of regular polygonal complexes in $\mathbb {E}^3$. In particular, the present paper establishes basic structure results for the symmetry groups, discusses geometric and algebraic aspects of operations on their generators, characterizes the complexes with face mirrors as the $2$-skeletons of the regular $4$-apeirotopes in $\mathbb {E}^3$, and fully enumerates the simply flag-transitive complexes with mirror vector $(1,2)$. The second paper will complete the enumeration.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.537
Threshold uncertainty score0.236

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.009
GPT teacher head0.248
Teacher spread0.239 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it