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Space filling with identical symmetrical solids

Published online by Cambridge University Press:  22 September 2016

J. E. Drummond*
Affiliation:
Australian National University, Canberra, Australia

Extract

In one dimension, a set of rods of equal length may be used to cover the line. In two dimensions, an area may be covered by joining up sets of identical symmetrical squares, equilateral triangles or regular hexagons. In three dimensions, there are at least four different symmetrical solids which can be packed together to fill space. Of these, the cube is most obvious, two others are moderately well known (see [1] for example), while I have been unable to find any record of the fourth solid.

Type
Research Article
Copyright
Copyright © Mathematical Association 1984

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References

1. Cundy, H. M. and Rollett, A. P., Mathematical models. Oxford (1974).Google Scholar