Models for Tetrahedra of All Possible Point Group Symmetries Mihai Horn and Sorin Mager University of Cluj-Napoca, Faculty of Technological Chemistry, R-3400 Cluj-Napoca, Romania Adalberl O r b h University of Cluj-Napoca, Faculty of Mathematics and Physics, R-3400 ClujNapoca, Romania Those teaching stereochemistry use geometrical figures as stereomodels to demonstrate the relevant properties of molecules. For organic stereochemistry the use of the tetrahedron-the simplest three-dimensional figure-has a long tradition. Starting with the regular tetrahedron with T d point symmetry (CaJ, one can accomplish a gradual desymmetrization by attaching different ligands to the otherwise eauivalent vertices of the tetrahedron (1.2). In this way one gets tetrahedra of Ca(Casb), CdCazbz), C.(Ca?bc). and C,(Cabcd) ~ o i nsvmmetries. t In addition to these rive types of tetrahedra there are three more of following symmetries: D2d(a2C= C = Ca2,biphenyl), CdabC = C = Cab, identical 2,2'-disubstituted biphenyls), and Dz (twistane)', the last two being chiral tetrahedra as well as CI. The use of these stereomodels is a common practice in modern organic stereochemistry ( I , 4-6). In the literature these figures are reoresented as two-dimensional ~roiections. and, as . " a result the three-dimensional architecture uften gets lost. The ins~ectionof three-dimensional models enables the student tdrecognize easily the symmetry properties and the s ~ a t i aarchitecture l of these models, a difficult task when using only two-dimensional projections, especially for the tetrahedra of D m 02, and C2 point symmetry, which do not follow from the T d tetrahedron by desymmetrization. This paper describes a method for making models of tetrahedra of all possible symmetry types. Only thin cardboard, transparent tape, a pair of scissors, a ruler, and a compass are needed. After the template (see figure) is cut from the cardboard (relative lengths of the edges according to the symmetry point group are taken from the table) the three triangles AB'C, BA'C, and AC'B are folded up, and edges AB1-AC', BA'-BC', and CB'-CA', respectively, are brought together and fixed with transparent tape. I t is useful to color code edges of the same length in order to facilitate the examination of the symmetry properties of the model. In the case of the chiral Dn. .. C?. .. and C, tetrahedra one can easily make both enantiomorphous mod'els hy folding triand e s AB'C. BAT. and AC'B forward and backward. resoec~~~
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Temlllate for the tetrahedra Relatke Dlmenslons of the SIXEdges of the Tetrahedraa Point
symmetry
AB
BC
AC
A'C = B'C
AB' = AC'
Proposed lengths (incentimetws):a = 5, b = 8. c = 7, d =
A'B = BC'
5.5, e = 7.5,snd f =
5.5.
~~
'Other examples of molecules belonging to the relatively rare point groups 4 and C2 are found in ref 3.
Literature Cited 1. Fre1og.V.; Halmchen. GHzIu.Chim.Acto 1972.55. 2581. 2. Ruch, E. Angem. Chrm.lnf.Ed.Eng1.1977.16.85. 3. Helmchen, G.;Hsas, G.:Prelog,V.Hdu. Chim.Acto 1973.56, 2255. 4. Preloe.V.Chzm.Briioin 1973.4. . . 382. 5. ~lelo;: V. Science 1976.193.17. 6. Pcelog, V.: Haimchen, G.Angou. Chem. Inl. Ed. Engl. 1982.21,567.
Volume 65 Number 12 December 1968
1073
