Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-16T02:54:38.632Z Has data issue: false hasContentIssue false

Some unusual space-filling solids

Published online by Cambridge University Press:  01 August 2016

P. Gailiunas*
Affiliation:
25, Hedley Terrace, Gosforth, Newcastle NE3 1DP

Extract

When identical copies of a solid can be packed together indefinitely to cover the whole of space and leave no gaps it is said to be space-filling. Usually only convex solids are considered in this context since, as Grünbaum and Shephard point out, non-convex space-filling solids can be generated from convex examples by making compensating additions and reductions, analogous to Escher’s modifications of plane tessellations. Nevertheless some non-convex space-filling solids are not obvious derivatives, and are interesting in their own right. Although the examples considered here have all been generated in the same way (to be described), their relation to other space-filling objects will also be considered.

Type
Articles
Copyright
Copyright © The Mathematical Association 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Grünbaum, B. and Shephard, G. C., Space filling with identical symmetrical solids, Math. Gaz., 69 (1985) pp. 117120.Google Scholar
2. Rouse Ball, W. W. and Coxeter, H. S. M., Mathematical recreations and essays (12th edn), University of Toronto Press (1974) pp. 152153.Google Scholar
3. Holden, A., Shapes, space and symmetry, Dover (1991) p. 165.Google Scholar
4. Williams, R., The geometrical foundation of natural structure, Dover (1979) pp. 230236.Google Scholar
5. Pearce, P., Structure in nature is a strategy for design (MIT) 1978.Google Scholar
6. Wells, A. F., The third dimension in chemistry, (Oxford University Press) (1956).Google Scholar