An Easily Constructed Bicapped Trigonal Prism Model Shukichi Yamana Department
of Kyoushoku Education, Kinki University. Kowakae, Higashi Osaka 577, Japan
A model of a bicapped trigonal prism t h a t is useful for teaching stereochemistry (for example of hydrazinium(+2) hexafluorozirconate, N2HsZrFd1 c a n be m a d e easily b y using two sealed, e m p t y envelopes. T h e steps (illustrated i n t h e figure) are given below. (1) The first figure shows the starting configuration (where the distances AD = DC = CE = EB), which is produced by steps 13 of a previously published article.2 (2) The lower part of the envelope is folded up at A so that the right corner B falls on the center Line (C). The corresponding point is marked F. (3) The lower part of the envelope is unfolded.' (4) A horizontal line perpendicular to the line (C) a t F, is drawn so that it crosses the lines (D) and (E) a t G and H.. resoeetivelv. (51 T h r middle point of theline the is marked I. (61 A horizontal line pcrpendirular to the line ( ( ' 1 at I, is drawn su that it crosses the left- and right-hand sides of the envrlopr at J a n d K, respectively. (7) The lower part of the envelope is folded up at I so that the lines I C and IKfall on the lines I J a n d (C), respectively. (8) On the original front ofthe envelope, the points corresponding to D, E , G, and H, are marked L, M, N, and 0 , respectively. (9) The lower oart of the envelone is unfolded. (1Oj The line MO is extended b i t h left- and rightward so that it crosses the left- and right-hand sides of the envelope and the lines (D) and (E) a t P , S, Q, and R, respectively. (11) The line L N is extended both left- and rightward so that it crosses the left- and right-hand sides of the envelope and the lines (D) and (E) at T, W, U, and V , respectively. (12) The right lower part of the envelope is folded up along the line LO so that the line I N falls on the line (C). On the front of the envelooe. . ,the m i n t corresoondine" to the N. is marked X. (13) The right lower part of the envelope is unfolded. (14) The intersection of the extension of the line VQ and the line XM is marked 1. (15) The intersection of the extension of the line UR and the line XO is marked 2. (16) The lower part of the envelope is folded up along the line JK. On the oriniual front of the envelooe, the points corresoondine to the points 1and 2, are marked 3 &d 4;respectiveli (17) The lower oart of the envelooe is unfolded. (18) The left upper part of the envelope is cut off along the zigzag course PMlG(D) composed of the four lines PM, MI, IG, and rm ~,(19) The right upper part of the envelope is cut off along the zigzag course S02H(E) composed of the four lines SO, 02, ZH, and (El. (20) The left lower part of the envelope is cut off along the zigzag course TL3D composed of the three lines TL, L3, and 30. (21) The right lower part of the envelope is cut off along the zigzag course E4NW composed of the three lines E4,4N, and NW. (22) The upper front of the envelope is folded Leftward a t H s o that the upper part of the line (E) falls on the LineHG. The intersection of the upper part of the line (D) and the newly produced crease is marked Y. (23) The upper front of the envelope is unfolded. (24) A horizontal line oer~endieularto the line (D) at Y. is drawn so that it crosses the line (E) at Z. (25) The unner oart of the envelooe is cut off alone the line YZ (26) On th; i a c c of the envelope, the points corresponding to the Y,
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Lao'), D H (i.e., DH*), ML (i.e., M*L*), ON (i.e., O*N*), 14 h..1'4'). ..and23 (i.e..Z13*). . . . (28) oblique lines are drawn to shade eight twin triangles (GIMI, IL3D, IE4N, and HI02 on the front; and G*I*M*I*,PL*3*D, I*E4*N*, and H*IS0*2* on the hack) and four redangles (PTLMand ONWS on the front; and PTL*M* and O*NsWS on the back). (29) The Left- and right-hand sides of the envelope are cut along the two lines P T a n d SW, respectively. (30) . . The orieinal oointsP. T. S. and W. are rewritten as (piand PI). ( ~ ~ a n d ~island ~ a ) .&),'&d ( W/ &d Wa), respectiv& accord: ing to the latitudes on which they are situated = front; b = hack). (31) Twosquares (YGHZon the front; and Y*G*H*Z* onthe back) are marked or and 01, respertiwly. (32) Eight regular triangles (C'IH. OIN, IDE,andAfLIm the front: and I'G'II'. I'O'N'. I'DE, and M'L'I' m the back) are marked b l , bz, bs, br, c,, cn, ca and cd, respectively. (33) The original hack of the envelope is unfolded downward along the line DE. (34) On the front of the envelope. the erght corners C,H. 0.N. fi:, I). L, and M, of the four triangles b , , h?. b 3 , and h,, are forced to approach each other so that the four lines GH, ON, ED, and LMform asquare and the four shaded twin triangles are folded inside. The sides are taped together to form a tetragonal pyramid having fuur slupesbl, b., b ,and b,. (35)On the original back uf tht. envelope, which has already heen cumerr D..E., unfoldrd aownward alonr the line DE. the eieht " N*, 0*, H', G*, M*, and L*, of the four triangles ca en, el, and c4, are forced to approacheach other so that the four lines DE, N'O*, HW*, and M'L* form a square and the four shaded twin triangles are folded inside. The sides are taped together to form a twin tetragonal pyramids having a common line and the two wings, an and as. ~
~
Next, the second envelope, of t h e s a m e shape a n d magnitude a s the first one used above, is employed to m a k e a trigonal prism. (36) The middle point of the line E'B' is marked F.A vertical line perpendicular to the base A'B'at F,is drawn and marked (R'). (37) The right part of the envelope is cut off along the line (F). (38) The right part of the front of the envelope is cut off along the lines F%' and (E'), and the corresponding rectangle on the hack of the envelope is folded inside along the line (E'). The side is taped to form an envelope of two-thirds width. (39) A trigonal prism model is made from this new envelope, by using the method shown in a previously published a r t i ~ l e . ~ (40) On the surface of this triganal prism model, the corners and faces are marked as shown in the figure. (41) This trigonal prism is intruded on the bottoms of the two component tetragonal pyramids which have been obtained by steps 1-35, folding the four shaded rectangles (PITILM, and ONWfSl of the left tetragonal pyramid; and T&M*L* and N*O*ShWh of the rieht tetrazonal nvramid) inside so that the three f&eb(ol of th; triganarprismfand =;and as of the twin tetragonal pyramids) are brought together and stacked in the order given by their numerals. (42) The sides are taped to produce the model mentioned in the title.
Z,G,H,M,O,I,L,N,1,2,3,and4,aremarkedY*,Z*,G*,H*, ' Koiic-ProdiC. B.; ShvnlEar, S.; Malkovi6. B. Acta Cryst. 1971,
M*, 0*, P,La,N*, I*, 2'. 3*, and 4*, respectively. (27) The envelope is folded both backward and forward along the lines GH (i.e., G'H*), GE (i.e., GaE),MN(i.e.,M*N"),LO (i.e.,
827, 638.
?Yarnana, S. J. Chem. ~ d u c1988,65,1071. . Yamana, S. J. Chem. Educ. 1984, 61,1055. Volume 66
Number 12
December 1989
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