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On the Contact Numbers of Ball Packings on Various Hexagonal Grids

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Istvan Szalkai

Metric Geometry · Submitted 19 Nov 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly the greedy algorithm.

how it is stated · asserted 0.99 read the record →

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arXiv ID1611.06394 (version 1)
Pith IDWLSMTA5S, Pith's permanent record of this paper and its review
CitationIstvan Szalkai. "On the Contact Numbers of Ball Packings on Various Hexagonal Grids." arXiv:1611.06394 (2016). https://pith.science/paper/WLSMTA5S
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,278 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.50 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.54 · compares with prior results 0.11 · mentions code or data availability 0.04.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly the greedy algorithm. We consider the octahedral grid, too.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly the greedy algorithm. contribution 1.00 0.96 0.19 asserted 0.99
s1 We consider the octahedral grid, too. contribution 0.99 0.66 0.03 asserted 0.88

What kind of paper the classifier reports this is: simulation study 0.96 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly the greedy algorithm. We consider the octahedral grid, too.

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