Space Structures pp 91-109 | Cite as
Exhaustive Enumeration of the Semiregular Two-dimensional Structures
Chapter
Abstract
In the preceding two chapters we generated semiregular structures by truncations and stellations of the regular structures found in Chapter 9. However, we shall find presently that we have by no means exhausted all possible semiregular structures in two dimensions. As we have found the means of determining the permitted connectivities to join the two-dimensional cells (polyhedra) into three-dimensional structures, it is important to ascertain that we are aware of all possible cells. To this purpose, we shall find all possible solutions of equation (9-5):
$$
\frac{1}
{{\overline r }} + \frac{1}
{{\overline n }} = \frac{1}
{2} + \frac{1}
{l}
$$
(9-5)
Keywords
Space Structure Regular Structure Exhaustive Enumeration Trivalent Vertex Vertex Valency
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Notes
- 1.Cf. Arthur L. Loeb: Color and Symmetry (Wiley, New York, 1971), pp. 5 and 6.Google Scholar
- 2.Donald Stover: Mosaics (Houghton Mifflin, Boston, 1966).Google Scholar
- 3.H. Freudenthal and B. L. van der Waerden: “Over een bewering van Euclides” (Simon Stevin, 25, 115-121).Google Scholar
- 4.M. Walter: On Constructing Deltahedra, to be published.Google Scholar
- 5.Robert Williams: Natural Structure (Eudaemon Press, Moorpark, California, 1972).Google Scholar
Copyright information
© Arthur L. Loeb 1991