An Easily Constructed Model of Twin Octahedrons Having a Common Line Shukichi Yamana' Faculty of General Education, Kinki University, Kowakae. Higashi Osaka 577, Japan Makoto Kawaguchi IDEC lZUMl Corporation, Mikuni-honmachi, Yodogawa-ku. Osaka 532, Japan
A model of twin octahedrons havine a common line which is useful for teaching stereochemist& (especially t h a t of comolex ions) can b e m a d e easilv b v w i n e a sealed. emotv envelope. ~ h ' steps e a r e illustraied i n thefigure a n d &eh below.
Edlor's Note: Over the past few years 5 . Yamana acd M. Kawaguchi have published a series of anicles containing instructions for making various wlyh&a models from a business envelope.These models have m y teachins applicetions h t are readily apparent, but we wish to point out that they also can be used in a more creative manner as pan of the holiday decorations that many departments like to display this time of yea^. The models can be made from colored construction paper or me heavier foiled wraooino oaoers bv. simolv . . cuhino out a rectanole with the same d mensmns as an open e w e ope, folang 01 over. ana sea ing it along the edges w m cei ophane tape. To make m a e lhan one cop, and also to avoid having markings on the final product, we have found it useful to make a panem from the original envelope model. Diredions for other models using the same technique can be found in:
1) The envelope is folded down the center lengthwise, and the middle point of the base AB is marked as C . 2) The lower part of the envelope is folded up so that the corner B falls on the center line. The new corner an the right-hand side of the envelope is marked as D. 3) A horizontal line is drawn oeroendieular ta the rieht-hand side . . of the envelope R I n, rrossmp. the center h e and the left-hand side of the envehpr st E and F, respectively. 4) The middle pointsof the lmrs AFand ilD are marked aa (:and H, respectively. 5) The extension of the line HE is drawn so that it crosses the lefthand side of the envelope at I. 6) The extension of the line GE is drawn so that it crosses the rirht-hand side of the envelooe at J. 7) '1.h lower part of rhr rnwlc& is foldrd up along rhc line IJ. 8) 'l'hecorre$punding point* on thr original obvcrsc, of C , A , C. H, 11, and E , arr markrd as f:', A', C', H', 11'. and F.", respectively. 9) The envelope is unfolded. 10) Cut off the upper part of the envelope along the line A'B'. 11) The rernainine oortion is folded both backward and forward alone ' thr linrs ~ ' ~ ~ ' " , ' lG l lJ'. ,CII. C'II', C ' J , 111, and C('. 12) .Separate the fronr and bark of thr lower pan oirhr rnvrlupr from each other by rutting the hase along the Ihc AH.
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Yamna, s., J. CmM. Eom., 45,245 (1968). Y m , 5. and Kawaguchi M., J. C m . EWC., 57,434(1980); 59, 196, 197, and 578 (1982); 60,548 (1983); and Ann. Rep. Res. Sci Educ.. KyoU, Univ. Educ., 9, 25 (1979); 10, 75 (1980). 13) The corresponding pointson the hack of the points C , E , El, and C', are mared as C*, E*, E'*, and C'*, respectively. 14) Separate the center line of the front from that of the back, pushing the left- and right-hand aides of the envelope together so that they meet back to back. 15) Two regular triangles, E'EJ and EHJ, are marked as a, and an, respectively. 16) The middle point of the line Er*E* is marked as K. 17) Cut the right-hand half of the envelope along the line K J
(=Kt). 18) Oblique lines are drawn to shade the six isosceles triangles,
C'H'C'*, HCC* (on the new front), C'G'C':, GCC* (on the new back), E'*JI, and JE*I on hoth sides. 19) While keeping the two points J and I touching each other.hack to back, the C and C' are pushed together until they meet, while the shaded triangles HCC*, GCC", and JE*I are folded inside. The sides are taped together to produce ,H' an octahedron.
' Author to whom correspondence should be addressed.
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Volume 61
Similarly, t h e other octahedron moiety can b e made by t h e following procedure. E
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20) While keeping the two points J and I touching each other back to hack, the C' and C'* are forced to approach and meet, folding the shaded triangles C'H'C'*, C'G'C'*, and E'*JI inside. The sides are taped together to produce the other octahedron. 21) Either of the octahedrons is turned so that the two faces a, and an are in contact. Finally, they are taped together to produce the model mentioned in the title. December 1984
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