Thomas C. W. Mak,' C. N. Lam, a n d O. W. Lau Chinese University of Hong Kong Shatin, N. T. Hong Kong
Drinking-Straw Polyhedral Models in Structural Chemistry
Three-dimensional models constructed from polyhedral units are particularly effective in the structural description and comprehension of isopoly and heteropoly anions, polyhedral clathrate hydrates, intermetallic compounds, minerals, and other non-mblecular crystalline solids considered from a coordinated-polyhedron viewpoint. Several papers ( I ) and books (2) have given detailed instructions for constructing various kinds of polyhedra from ball-and-spoke components, plastic tubing with either flexible connectors or rigid 'valence clusters,' cocktail picks, metal wire, cardboard, acrylic plastic (Plexiglas, Lucite, Perspex) sheets, and rigid polyurethane. Manufactured hollow polyhedra in Plexiglas and in polystyrene are also available. However, apart from considerations of cost, durability, and tediousness in construction, considerable difficulty may be experienced in making use of the above materials in building scaled models of complex crystal structures based on space-filling assemblies of different kinds of polyhedra, which are not necessarily regular or semi-regular and mav even be distorted. For example, the building blocks of polyiedral clathrate hydrates include a fascinating variety of convex polyhedra (3). the construction and assembly of . . which present very real problems to all but the experienced model builder. Ideally the polyhedral components should be sufficiently
sturdy and yet flexible enough to take up slight distortions arising from the packing of a large number of imperfectly made polyhedral units in order to satisfy the space-filling requir&& Open, transparent models have a decided advantage over solid ones as structural details and symmetry elements can he seen a t a elance. T o emphasize certain salient features or simply for attractive appearance, suitable colors rnav he annlied to Dart or all of the model: and it should be possible to carry out this step with ease. Furthermore, it is desirable to keep the required skill, time, and cost involved in model construction to a minimum. In the present paper we describe a neat and surnrisinelv simple procedure for constructing polyhedral models w&ih comes ;lose to meeting the above criteria for a versatile and inexpensive method. The ideal material turns out to he plastic drinking straws, the type universally used for milk and other bottled and canned beverages. Straws made of polyethylene are translucent and flexible. whereas the ~olwroovlenevariety is stiffer and comes in an opaque white-with cbiored strip& running along its length. In our experience the cheaper polyethylene straws are easier to work with; coloring may be done with marking pens on the finished model or, in a more elegant and permanent way, by rolling up a strip of colored paper or cellophane and inserting it lengthwise into each straw prior to model assembly. ~~
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Constructional Details 1 ) Initially, a rectangular piece of cardboard or thin aluminum plate is prepared. The dimensions of this 'template' sets two possible edge-lengths to be used for constructing the polyhedra. 2) A polygonal face is made by folding a plastic straw repeatedly around opposite sides of the template (Fig. la) and then inserting one end of the straw into the other (Fig. lb). 3) To join two or more faces together, a resin-type adhesive2diluted with toluene is lightly applied to the'sharp edge'of a side in each (a) (b) Id face. When the adhesive has almost dried. the edaes are carefullv brought together in the proper orientation (Fig.3~).In this way Figure 1. (a) Folding a drinking straw with the aid of a template. (b) lnseltingone any polyhedron may be gradually assembled from the necessary end of the straw into the other to form a polygonal face. (c) Polyhedron being number of faces (see table). assembled by cementing together the sharp edges of polygonal sides. 4) A given crystal or molecular structure ma). be rmsrrurtrd Iq simpl? cementan:: t o z t t h v r completed pulvhrdml units. Hvnwrr, wxc-i~llmc modrli ill better if redundant faces common to neighboring polyhedra are eliminated, and in such cases it is advantageous to build up the model by the successive addition of polygonal faces at the later stages. Any conspicuous imperfection in the finished modelshould be rectified by manipulating those joints where distortion shows up to a great extent. 5) A very large model constructed entirely from polyethylene straws may sag appreciably under its own weight. This difficulty is overcome by building the model with a judicious combination of polyethylene and polypropylene straws. The rigidity of large, open polyhedra such as the truncated cuboctahedran ~tlwtublr~cnn hegrrarlystrrnrthcned 11, ouslng lmlyethyltlnr qrmus inwttcd Figure 2. Rhombohedral-12 boron (~1-lorm)(6). The structureconslstsof a slightly deformed cubic close-packed with thln slumiuun> strps for the I~ which are linked by sl3ghtly longer intericosahedral B-B bonds in the array of nearly regular 8 ,icosahedra. tagonal and hexagonal faces Same layer and shorter ones between neighboring layers. ~
438 1 Journal of Chemical Education
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Polyhedral Models
We have constructed scaled models of a range of molecular and crystal structures based on various ways of packing the regular and semi-regular polyhedra listed in the table. Matched pairs of stereoscopic photographs (4) of two representative straw models3 are shown in Figures 2 and 3, which may he examined with the aid of inexpensive viewers consisting of plastic lenses mounted in cardboard holders. These stereoarams (7). The host structure of this clathrate may he and used in conjunc- Figure 3. The peralkyiammonium salt hydrate [i-CsH~~]N+FF.3SH20 tion with the ones displayed by Wells in is constituted from alternate layers o f face-sharing pentagonal dodecahedra and pentakaidecahedra, the intelvening space being filled by columns of tetrakaidecahedra. The model shows a boltom layer of dodecahedra, his introductory text On structural a top layer of pentakaidecahedra, and venical columns of tetrakaidecahedra. chemistry (5). T h e assembly of drinking-straw models is easy and reasonably rapid; the finished products are cheap hut precise, Acknowledgment light yet durable, functional and also aesthetically pleasing. T h e authors wish to express their appreciation to Mr. The technique is applicable to the construction of all kinds Yuk.Sung Lau for constructing some of models and to polyhedral and "ystal and as such Kam-Wah Lau for assistance in preparing the stereograms. should he of special interest to crystallographers, miueralogLiterature Cited ists, and solid-state physicists as well as to chemists. (1) Mwmh, M. E., and Dsugherty, K. E., J. CHEM. EDUC.,52.239 I1975):h,C.
Common T y p e s of Convex P o l y h e d r a in t h e Construction of Straw M o d e l s Kinds and numbem of POiygonal face.
Polyhedron tetrahealon truncated tetrahedron octahedron truncated octanearm cuboctahedron truncated cuboctanearm i~o~ithedr~n pentagonal dodecahedron tetrakaiaecahearon pentakaidecahedron hexakaidecanedron
Symbola 3$ 3.6'
4
4
3* 4.6'
8
(3.4)' 4.6.8
8
3= 53
5'. 5 ' 3 5'. 5'.6 5'.5'.6
000
a
4
6
N.,Lau,
0. W., La". Y. S.. and Mak, T. C. W.. J. CHEM. EDUC.. 53.740 (1976). (2) Cundy, H. M.. and Rollatt, A. P.,"Mathomatical Models." 2nd Ed., Oxford Univcnify
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Press. Landon, 196L; Wenninger, M.J.."Pdyhedron Models." CambridgeUniveraity Press. London. 1970: Waifon, A.. "The Use af Models in Stereochemlstry" in Vol. 4 of "Progress i n Stereochemistry,l'(Edilors: Aylett. B.J., and Harris, M. M.), ButLerworthr, London, 1969; Wells. A. F.. "Models in Structural Inorganic Chemistry," Oxford University Prass. hndon. 1970:Holden. ~.,"Shapes,Space. a.dSymmdry." Colvmbis University P~ess, New York, 1971. 181 Jeffrey.G. A,, and M C M U ~ R. ~ ,K . . - T ~ * ciathrate nydrates"in VOI. B ~ I in Inorganic Chsmiitry,"(Edrioc Cotton, F. A.1 Wiiey-Interscience,New York, 1961; Jofiro~,G.A.,A
