The IUPAC Systematic Names of the Regular An exercise in organic chemistry nomenclature Albert Moyano and Felix Serratosa Universitat de Barcelona. Barcelona-28, Spain Pelayo Camps and J o s e p M. Drudis Universitat Autonoma de Barcelona. Bellaterra (Barcelona), Spain Professor P. E. Eaton, from The University of Chicago, has recently published a rather inspired review on the synthesis of regular polyhedranes ( I ) . Using his own words: "For the organic chemist, hearing the beat of a different drummer, translation of the Platonic solids into real molecules has always meant synthesis of tetrahedrane, cuhane and dodecahedrane." As active research chemists engaged in some synthetic approaches to dodecahedrane, in this short communication we wish to show: (11 The eeometrical bases from which Eaton's assertion comes, and (2) A very simple procedure to asslgn IUPAC systematic names to all the polyhedranes, as well as other polyeyclie hydracarhons, such as prismanes (21.
Figure 1. The regular polyhedra.
First: The classical Euler's law (3), C+F=E+2
(11
which states that "the sum of the number of corners and faces of a polyhedron is equal to two more than the total number of edges," provides a suitable method to calculate which ones of the polyhedral structures are possible for C,H, bydrocarbons. From the point of view of an organic chemist, Euler's law can he restated as (4): N (C atoms) + N (faces) = N (C-Cbnnds) + 2
(2)
where N is the number of the items named in parentheses. C,H, polyhedral structures are possible only if, N (C-C bonds) meeting at each C atom N (Catoms) (N faces) - 2 = = N (C atoms)/:!
+
13)
Restricting i t to the regular or Platonic solids, we can see, from Table 1, that only tetrahedrane, cuhane, and dodecahedrane (Fig. 1) meet the condition stated in eqn. 3, in agreement with Eaton's assertion. Second: Now suppose that a given polyhedron is resting on one of its faces and that it is viewed from below. Because of the perspective effects, all the other faces appear to lie within the one nearest the observer, as shown for a cube in Figure 2.
Figure 2. Suppose that a given polyhedron is restlng on oneof lts faces andlhat it is viewed from below. As a result of the perspective effects, all the other faces appear to lie within the one nearest the observer.
This type of diagram is called Schlegel diagram (3)(5),and from the point of view of an organic chemist it is a very convenient way of representing any polyhedrane (Fig. 3) because: (1) It shows at once the numher of primary ring.9 (61, which is coincident with the number of rings according to IUPAC rule A-32.12 (7). (2) Allows determination of the main ring, which according to rule A-32.31
Table 1. Regular or Platonic Solids and Eaton's Assertion Regular polyhedron
type of face myon
o faces
n comers
n edges meeting at each corner
Tetrahedron (a) Octahedron (b) Hexahedron ( c ) Icosahedron (dl Dodecahedron (el
3 3 4 3 5
4 8 6 20 12
4 6 8 12 20
3 4 3 5 3
126
Journal of Chemical Education
polyhedrane CH l4
-
tetrahedram
C.H.cubane
-
C z 0 H 2dodecahedrane ~
Table
Polyhedrane (nrings)
2.
Systematic N a m i n g for A l l T h r e e Regular Polyhedra numbering main bridge secondary bridges
main ring (n C atoms)
IUPAC systematic name (rule A-32) tricyclo[l.l.0.024] butane
4-membered ring = butane
TETRAHEDRANE 3 rings = tricyclo
CUBANE
5 rings = pentacyclo
DODECAHEDRANE
I 1 r i m s = undecacvclo
8-membered ring = octane
20-membered ring = icasane
(a) shall contain as many carbon atoms as possible, two of which must serve as bridgeheads for the main bridge; (bj the main bridge shall be as large as possible; (cj the main ring shall be divided as symmetrically as possible hy the main bridge; id) the superscripts locating the other hridges shall he as small as possible. (3) Using the above criteria, the systematic name, according to the rules A-32.11, A-32.12, and A-32.13, results for all three regular polyhedra (Table 2).
Literature Cited (1) Eaton. P. E., Teliohedion,35,2189 (1979). (2) Cf, Schuitz. H. P. J. Org Chrm.,30,1361(1966). (3) Web. A. F.,"The Third Dimenaion in Chemistry:'Oxford a t the Claiendon Press, 1956, "" mi'
"
-
.
.
~ ~
drocarbons. (6) Carey, E. J.. nowe.W. J., 0 % H. W., Pensak,D. A,, and Peterson, C., J. Arne,. Chrm. Soc.,97,6116 (1976). (71 Rigaudy, J., and Klesney, S. P.. "IUPAC, Nnmenclature ofOrganieChemistry,Sections A, R. C, D. E, F, and H, 1979 Edition? Pergamon Press, pp. 3 2 3 4 .
e C
Figure 3. The regular polyhedra: the Schlegel diagrams.
Volume 59
Number 2
February 1982
127
