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 to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Goldberg, M., ‘On the Space-filling Hexahedra’, Geom. Dedicata 6, 99–108 (1977).
Goldberg, M., ‘Several New Space-filling Polyhedra’, Geom. Dedicata 5, 517–523 (1976).
Federico, P.J., ‘Polyhedra with 4 to 8 Faces’, Geom. Dedicata 3, 468–481 (1975).
Federico, P.J., ‘The Number of Polyhedra’, Philips Res. Repts. 30, 220–231 (1975).
Kershner, R.B., ‘On Paving the Plane’, Am. Math. Monthly 75, 839–844 (1968).
Schattschneider, D., ‘General Paving Pattern of Richard James III’, Private communication.
Fejes Tóth, L., ‘What the Bees Know and What They Do Not Know’, Bull. Am. Math. Soc. 70, 468–481 (1964).
Wood, D.G., Space Enclosure Systems, The Orderly Sub-division of the Cube, The Ohio State University, 1973.
Critchlow, K., Order in Space, Viking Press, New York, 1970.
Stein, S.K., ‘A Symmetric Star Body that Tiles as a Lattice’, Proc. Am. Math. Soc. 36, 543–548 (1972).
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
- Equilateral Triangle
- Triangular Prism
- Hexagonal Prism
- Reidel Publishing Company
- Honeycomb Cell