Skip to main content
Log in

On the space-filling heptahedra

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

A space-filling polyhedron is one whose replications can be packed to fill three-space completely. The space-filling tetrahedra, pentahedra and hexahedra have been previously investigated. The search is here extended to the convex space-filling heptahedra.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliography

  1. Goldberg, M., ‘On the Space-filling Hexahedra’, Geom. Dedicata 6, 99–108 (1977).

    Article  MATH  Google Scholar 

  2. Goldberg, M., ‘Several New Space-filling Polyhedra’, Geom. Dedicata 5, 517–523 (1976).

    Article  MATH  Google Scholar 

  3. Federico, P.J., ‘Polyhedra with 4 to 8 Faces’, Geom. Dedicata 3, 468–481 (1975).

    Article  MathSciNet  Google Scholar 

  4. Federico, P.J., ‘The Number of Polyhedra’, Philips Res. Repts. 30, 220–231 (1975).

    MATH  Google Scholar 

  5. Kershner, R.B., ‘On Paving the Plane’, Am. Math. Monthly 75, 839–844 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  6. Schattschneider, D., ‘General Paving Pattern of Richard James III’, Private communication.

  7. Fejes Tóth, L., ‘What the Bees Know and What They Do Not Know’, Bull. Am. Math. Soc. 70, 468–481 (1964).

    Article  Google Scholar 

  8. Wood, D.G., Space Enclosure Systems, The Orderly Sub-division of the Cube, The Ohio State University, 1973.

  9. Critchlow, K., Order in Space, Viking Press, New York, 1970.

    Google Scholar 

  10. Stein, S.K., ‘A Symmetric Star Body that Tiles as a Lattice’, Proc. Am. Math. Soc. 36, 543–548 (1972).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goldberg, M. On the space-filling heptahedra. Geom Dedicata 7, 175–184 (1978). https://doi.org/10.1007/BF00181630

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00181630

Keywords

Navigation