Molecular Models Constructed in an Easy Way Part 1. Models of Tetrahedron, Trigonal Bipyramid, Octahedron, Pentagonal Bipyramid, and Capped Octahedron Fu-cheng He, Lu-bin Liu, and Xlang-yuan Li Chengdu University of Science and Technology, Chengdu, Sichuan 610065. The People's Republic of China
A series of articles containing instructions for making polyhedron models from a businis8 envelope has been published in t h k Journol.'~'Hecently I. Jimenez and co-worken proposed a method for making simple geometric models starting from a continuous strip.3 This fresh idea is instructive, hut unfortunately the models built by their proposed ~roceduresare so loose as in some cases to be unable to maintain the necessary shapes. In the present as well as successive articles, we introduce a n improved technique for makine various molecular models from a strio oaoer. The . of . generay procedure for making a model of a single poGhedron includes the following elementary operations: (1) Make folds on a paper ribbon. (2) Use the left portion of the folded paper ribbon to form a skeleton of the polyhedron. (3) Wind the remaining portion of the paper ribbon around the skeleton. (4) Insert the end of the paper ribhon into aslot along an edge of the model to finish the operations.
Particularly noteworthy is the winding operation with the paper ribbon that makes the model tight and fixed; therefore, i t needs to be elaborately designed. T o develop the technique to make models complex in structure, polyhedral units (similar to the models of those corresponding polyhedra) are made from separate paper ribbons, and the whole model is constructed by assembling the polyhedral unite together. This obviously makes an easy and economical wav for constructing structurallv complex models. ~oreover,"onemight cre& something new by using various polyhedral units as building blocks. In this article i t can be seen that the models mentioned in the title can easily be made from a strip Examples - of paper. -~ for making the models complex in structure will be given in the successive articles.
(1)A strip of paper (-23 cm long and 3.5 cm wide) is folded down
the center lengthwise to produce a straight fold ahout 4 cm in length at the left end of the paper rihhon (Fig. l(a)). (2) The left end of the paper rihhon is folded dawn so that the comer aa falls on the center line. This operation leaves on the paper rihon a concave fold a m (Fig. l(h)). (3) Let the fold a m coincide with the upper edge of the paper ribbon. Thus a concave fold, aza3, is made (Fig. l(c)). (4) Let the fold axas coincide with the lower edge of the paper ribbon so that a concave fold, as-, is made as well (Fig. l(d)). (5) The other folds on the paper rihhon are produced hy the repeated operations as described in steps 3 and 4. Notice that in Figure I(e) the dashed lines refer to the concave folds and the dashand-dot lines (%a?,avaa, . . .,allaid refer to the convex folds on the paper ribbon. 16) Let the fold a,an coincide with the fold a.ac so that the first four equilateral tr&gles on the paper ribbon form a tetrahedral skeleton (Fig. I(f)). (7) Let Aa&al coincide with Aa~azaaand Aamas coincide with Ayasa? so that Aasasai is sandwiched between Aalalas and Aasa7as (Fig. l(g)). (8) Wind the remaining portion of the paper rihhon around the tetrahedral skeleton until Aasarnal~meets Aa?arsn, and then insert Aaloalla~z into the slot along aaa7 (Fig. l(h)j. .' (9) Finally press Aasaloall to coincide with. Aaza3ad to produce a tetrahedron model (Fig. l(i)). ~
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I t can be seen that a tetrahedron model made from a strip of paper has five slots along its three edges. These slots are useful for combining a tetrahedron model with others. Trlgonal Blpyremld Models A model of a trieonal biovramid mieht be of interest to students as well as teachersiince the known ABs complexes are mainly trigonal bipyramidal in structure. The steps for
A Tetrahedron Model A tetrahedron model is useful for teaching the stereochemistry of many molecules and ions. The typical examples are as follows:
The Steps for making a tetrahedron model from a strip of paper are illustrated in Figure 1and given below. FToject supported by the National Sclence Foundation of China. Yamana S. J. Chem. Educ. 1988, 45, 245; 1984, 61, 449-450,
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1055,1056,1058-1059: 1985, 62, 1068-1069, 1088-1089. Yamana S.; Kawaguchi M . J. Chem. Educ. 1980, 57,434: 1982, 59, 196-197.578-579; 1983, 60,548; 1984, 61, 1053, 1054. Jimenez I.; Pastor G.; Torres M. J. Chem. Educ. in press.
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Journal of Chemical Education
Figure 1. A tetrahedron model made horn a strip of paper
isosceles triangles (Fig. 3(a)). T h e other steps for making such a model are illustrated in Figures 3(b), 3(c), and 3(d). An Octahedron Model An octahedron model is useful for teaching the stereochemistry of complexes because all ABs complexes for which the structures have been determined are octahedral or nearly so. The steps for making a model of an octahedron from a strip of paper are illustrated in Figure 4 and given below.
Figure 2. A model of a Oigonal bipyramld made horn a sfrip of paper ulm concave folds forming 14 sgullateral lrlangles.
making a trigonal bipyramid model are illustrated in Figure 2 and described below. (1) A strip of paper (-31 cm long and 3.5 em wide) is folded as
shown in Figures l(a), l(b), l k ) , and Ud), so that the concave folds make 14 equilateral triangles on the paper ribbon. (2) Let the fold a m coincide with the fold a"%. Thus the first five equilateral triangles on the paper ribbon form a skeleton of a trigonal bipyramid (Fig. 2(a)). (3) Let A%a7ascoincide with Aalaza3and wind the remaining portion of the paper ribbon around the skeleton until Aalaamals meets Aasasai (Fig. 2(b)). (4) Finally insert Aallalsals into the slot along asall and press Aalaallala to coincide with Aasasa7 (Fig. 2(c)). Then we have a model of a triganal bipyramid with six slots along its four edges (Fig. 2(d)).
It should he noted that we may construct a model of a trigonal hipyramid having much shorter axial length if the concave folds on the paper ribbon (3.5 cm wide) are made a t the first step in such a way that they form 16 rectangular
(1) A strip of paper (-49 cm long and 3.5 cm wide) is folded as shown in Figures l(a), Ub), l(c), and l(d) so that the foldsmake 23 equilateral triangles an the paper ribbon. Notice that asao, asa~o,.. .,als aI6, a,& are convex folds and the other folds are concave ones. (2) Let the fold alaz coincide with the fold mas so as to produce an octahedral skeleton (Fig. 4(a)). (3) Let Aavasag coincide with Aa~azasand Aasasa~ocoincide with Aa.rws so that Anmas is sandwiched between Aa1aza3 and Aasaseio (Fig. 4(b)). (4) Wind the remaining portion of the paper ribbon around the octahedral skeleton until Aa~sa,sa~.i meets Aasamall (Fig. 4(c)). Notice that in Figure 4(c) alsa17 is a convex fold and a17ala, alaals, . . .,azms, are concave folds. (5) With the aid of the fold alsal?, Aa~salra~a is folded to coincide with Aalsalsan Press Aalaalsa17so that Aa~ealmsissandwiched between Aalsa~sa~i and Aasa~oa~l (Fig. 4(d)). (6) Winding the paper ribbon around the octahedral core a n d f d ly inserting the last equilateral triangle Aa23a2razsinto the slot along alsalv (Fig. 4(e)),we obtain an octahedron model withnine slots along its seven edges. ~
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A Model ot a Pentauonal Blpyramld Students as well as teachers may fmd i t interesting to make a pentagonal bipyramid model that is related t o the structures of a number of compounds, such as IF%B?H:-, ZrF:-, V(CN):-, etc. The steps for making a model of a pentagonal bippamid from a strip of paper are illustrated in Figure 5 and given below. (1) astrip of paper (-57 cmlong and 3.5 em wide) isfoldedas shown
in Figures l(a), l(b), l(c), and l(d) so that the concave folds make 27 equilateral triangles on the paper ribbon. (2) Let the fold ala2 coincide with the fold asas so thattheleft seven equilateral triangles on the paper ribbon form a skeleton of a pentagonal bipyramid (Fig. 5(a)). (3) Let Aa8asalo coincide with Aala2a3, and wind the remaining portion of the paper ribbon around the skeleton until Aazsa~?a%s meets Aa~sanoazl(Fig. S(b),Nc), and 5(d)). (4) Finally insert Aa2maazg into the slot along alsaa to produce a pentagonal bipyramid model (Fig. 5(e)).
A Model of a Capped Octahedron ~
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A model of a capped octahedron, which is necessary for teaching the stereochemistry of cluster compounds such as Figure 3. A model of a hlgonal blpyramld made fmm a sblp of p a p wlm concave folds formlng 16 rectangular ls~scelesOiangles.
Figure 4. An octahedron model made fmm a shlp of paper.
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Figure 5. A pentagonal blpyramld model made from a shlp of paper. Volume 67
Number 7
July 1990
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Figure 6. A capped actahedmn model made from a snip of paper Figure 7. A photograph of the six models made from a strip of paper (3) Let Aaaasa~ocoincide with Aa~azaaand Aana~palscoincide with
MoXa.3PR3 (x = halogen atoms, R = alkyl groups), can easily be made by using a strip of paper. The steps for making such a model are illustrated in Figure 6 and described below. (1) A strip of paper (-49 em Long and 3.5 cm wide) is folded in such a way that the concave folds make 23 equilateral triangles (i.e., the same DaDer . . ribbon used for makine~.an octahedron model except changing all the convex folds to concave ones). (2) Let the fold am! coincide with the fold a,a,, and press a, leftward su as to obtain a capped octahedron rkeleum (Fig. 6(a)). ~
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Journal of Charnlcal Education
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Aasasa7 ao that the gap Aalasasa7 is just covered (Fig. 6(b)). (4) Wind the remaining portion of the paper ribbon around the skeleton, and finally insert Aa~~azdazs into the slot along alealato obtain the model (Figs. 6(c) and (d)). T h e six models made from a strio of DaDer have been photographed (Fig. 7). Models of closid triangulated polvhedra, such as that of rhombohedron. b i c a o ~ e dArchimideian &tiprism and icosahedron, can also be made from a strip of paper hy using the same technique.
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