An Easily Constructed Monocapped Octahedron Model Shukichi yarnanal Department of Kyoushoku Education. Kinki University, Kowakae, Higashi Osaka 577, Japan
A model of a monocapped octahedron having three top angles of about 90 a t h a t i s useful for teaching stereochemistry (for example of heptamordinate complex triddiphenvl~ro~anedionato)aauoholmium, Ho(CsH&OCHCOC&h -. H ~ O ?can be made easily by using two sealed, empty envelopes. T h e principle of t h e method is first t o produce a model of a trigonal pyramid having three top angles of about 90 ' a n d amodel of a n octahedron a n d next t o combine them with each other t o yield t h e model given i n t h e title. The steps (illustrated in t h e figure) a r e given below.
.
(1) The first figure shows the starting configuration which is produced by steps 1-6 of a previously published article? The two lines narallel with the l e R and right-hand sides
of the envelope, are marked ( X ) and (E? respectively, according to the points through which they pass. (2) The right lower part of the envelope is folded up at D so that the IineDC falls on the IeRhand side of the envelope. The new comer on the right-hand side of the envelope is marked I. (3) The right lower part of the envelope is unfolded. (4) The intersection of the two lines DZ and (HI is marked J. ( 5 ) A horizontal Line, perpendicular to the line ( H ) at J is drawn so that it cmsses the l e R and right-hand sides of the envelope and the line ( E )a t K,M, and L, respectively. (6) The upper part ofthe envelope is cut off along the lineKM. (7) On the back of the envelope, the points corresponding to J, L, and G are marked J*, L*,and G*, respectively. (8) The lower parts ofthe envelope are cut offalong the zigzag course DHGB, composed of the three lines DH, HG, and GB. The original polntHis rewritten as ( H p d H baccording to the sides an which they are situated (f = fmnt; and h = back). (9) The three regular triangles (DHfG on the front; GBG* on both sides; and DHbG* on the back) are labelled al, az, and a,, respectively. (10) Oblique lines are drawn to shade three triangles (JGM I on the front; J*G*M on the C hack; and J D J X on both D I I sides). I (11) The envelope is folded both backward and forward along A H E B the lines D J (i.e., DJ*), J G (i.e., J*GX),GM (i.e., GXM), DG (i.e., DG*), GC (i.e., GXC),andLG (i.e., LXG*). (12) The right- and left-hand sides of the envelope are pushed together so that the three lines (DG, GG*, and DG*) form a regular triangle. (13) Three points J, M, and J* are pushed together and the three shaded creased triangles (JGM, MG*JX, and JDJ*) are folded inside. The sides are taped together to produce the upper half of a
-&b-
1030
Journal of Chemical Education
trigonal pyramid having three top angles of 90". Next, the second envelope of t h e same shape and magnitude a s the first one used above, i s employed to produce an octahedron. (14) By the same steps a s those indicated in the previously published a r t i ~ l e s ? a~ model of an octahedron is made, and its apexes are marked P, Q,' R', S, T; and U', res~ectivelv. (15) The three ngular triangles sumoundii~the regular triangle PR'S' rPQ'X', R'iiS', and PS'T, are mnrktd a',, a'z, and a's, respeetively. (16) This octahedron model is intruded on the bottom of the model of a trigonal pyramid having three right-angled triangular faces (which was obtained by steps 1-13) so that the three faces a'l, a'z, and a', of the former are covered by the three faces al, az, and a, of the latter, respectively. The sides are taped to produce the model desired. 'Address correspondence to: 27-2 Momoyama Tsutsui iga Nishimachi, Fushimi-ku, Kyoto 612, Japan. 2Zalkin, A,; Templeton, D. H.; Karraker,D. G., Inorg. Chem. 1969, 6, 2680. 3Yamana, S. J. Chem. Educ. 1984,61,1054. 4Yamana, S.; Kawaguchi, M. Annual Repoil of Researches in Science Education, Kyoto University of Education: Kyoto, 1981; No. 11, p 15: Australian Chemistry Resource Book, 1987,27. =Yamana,S. Internat. Newslet. on Chem. Educ. (IUPAC)1989,31, 11.
