Skip to main content
SpringerLink
Log in

The number of edges per face in a large aggregate of space-filling, random-sized, randomly arranged polyhedra

  • Short Note
  • Published:
Journal of the International Association for Mathematical Geology Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Bernal, J. D., 1964, The structure of liquids: Royal Soc., London, Proc. A, v. 280, no. 1382, p. 299–327.

    Google Scholar 

  • Bernal, J. D., and Finney, J. L., 1967, Geometry of random packing of hard spheres: Disc. Faraday Soc., no. 43, p. 62–69.

    Google Scholar 

  • Coxeter, H. S. M., 1969, Introduction to geometry (2nd ed.): John Wiley & Sons, New York, 469 p.

    Google Scholar 

  • Desch, C. H., 1919, The solidification of metals from the liquid state: Jour. Inst. Metals, v. 22, no. 2, p. 241–276.

    Google Scholar 

  • Groemer, H., 1971, Continuity properties of voronoi polyhedra: Monatshefte f. Math., v. 75, pt. 5, p. 423–431.

    Google Scholar 

  • Hulbary, R. L., 1944, The influence of air spaces on the three-dimensional shapes of cells in elodea stems, and a comparison with pith cells of ailanthus: Am. Jour. Botany, v. 31, no. 9, p. 561–580.

    Google Scholar 

  • Kelvin, Lord (T. W.), 1887, On the division of space with minimal partitional area: Phil. Mag., v. 24, no. 151, p. 503–514.

    Google Scholar 

  • Mason, G., 1971, A model of the pore space in a random packing of equal spheres: Jour. Colloid & Interface Sci., v. 35, no. 2, p. 279–287.

    Google Scholar 

  • Matzke, E. B., and Nestler, J., 1946, Volume-shape relationships in variant foams. A further study of the role of surface forces in three-dimensional cell shape determination: Am. Jour. Botany, v. 33, no. 2, p. 130–144.

    Google Scholar 

  • Meijering, J. L., 1953, Interface area, edge length, and number of vertices in crystal aggregates with random nucleation: Philips Research Reports, v. 8, rept. 218, p. 270–290.

    Google Scholar 

  • Rhines, F. N., Craig, K. R., and DeHoff, R. T., 1974, Mechanism of steady-state grain growth in aluminum: Metallurg. Trans., v. 5, no. 2, p. 413–425.

    Google Scholar 

  • Rogers, C. A., 1964, Packing and covering: Cambridge Univ. Press, Cambridge, 109 p.

    Google Scholar 

  • Smith, C. S., 1964, Some elementary principles of polycrystalline microstructure: Metallurg. Reviews, v. 9, pt. 33, p. 1–48.

    Google Scholar 

  • Williams, R. E., 1968, Space-filling polyhedron; Its relation to aggregates of soap bubbles, plant cells, and metal crystallites: Science, v. 161, no. 3838, p. 276–277.

    Google Scholar 

  • Williams, W. M., and Smith, C. S., 1952, A study of grain shape in an aluminum alloy and other applications of stereoscopic microradiography: Jour. Metals, v. 4, no. 7, p. 755–765.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geology, University of Toronto, Canada

    D. F. Watson

Authors
  1. D. F. Watson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Watson, D.F. The number of edges per face in a large aggregate of space-filling, random-sized, randomly arranged polyhedra. Mathematical Geology 7, 349–354 (1975). https://doi.org/10.1007/BF02081706

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02081706

Keywords

Search

Navigation