An Easily Constructed Pentagonal Pyramid Model Shukkhi Yamana Faculty of General Education, Kinki University. Kowakae. Higashi Osaka 577. Japan
A model of a pentagonal pyramid, which is useful for teaching stereochemistry (for example t h e hexahorane B6H10)'can he made easily hy using a sealed empty envelope. T h e steps (illustrated in the figure) are given (1)The envelope is placed lengthwise, and the middle point of its left-hand side AC is marked D. (2) . . Twomiddle mints of the lines AD and DC are marked E andF, respectively.. (3) Three middle points of the lines AE, ED, and DF, are marked G,H, and I, respectively. (4)Four parallel lines DM, HL,EK, and DJ with the line IB, are drawn so that each of them passes D, H, E, or G and intersects the base AB at the points M, L, K,and J , respectively. (5) The middle point of the line MB is marked N . (6) The middle point of the line MN is marked 0 . (7) Four parallel lines with both sides of the envelope, (4,(K),(L), and (M), are drawn so that each of them passes the points J, K, L.and M. resoectivelv. (8) ~'hnrm&liine, pe;pendirular ro the left-hand side of the envelope at H, is drawn so that it crosses the lines (K)and ( M ) and the right-hand side of the envelope at P, Q. and R, rerpectively. (9) The intersection of the lines H R and I 0 is marked S.
(10)The lower part of the envelope is folded up leftward at H so that the paint Pfalls on the Line (J)and its correspondingpoint is marked T. (11)The lower part of the envelope is unfolded. (12)The Lower part of the envelope is folded up rightward at H 8 0 that line (4 passes the paint S,and its corresponding point is marked U. (13) The lower part of the envelope is unfolded. (14)A horizontal line, perpendicular to line (4at T,is drawn so that it crosses the left- and right-hand sides of the envelope and line (L)at V,X,and W,respectively. (15)A horizontal line, perpendicular to line (4 at U,is drawn so that it crosses the Left- and right-hand sides of the envelope and line (L)at Y,Z' and Z, respectively.
-
'
Hirshfeld, F. L.: Erlks, K.: Dlckerson, R. E.; Lippert. Jr.. E. L.: Lipscomb, William N. J. Chem. Phys., 1958, 28, 56. For the rationale for maklno various Dolvhedra models from a business envelope. see the ~ b s t i c t ( ~2.32jof 0. me 31sl lnlernatlonal Congress of Pure and Applied Chernislry (July 13-18. 1987, Sofia. Bulgaria). ~
~~~~
!Y I
l
I
i
-4T-I-*!--x
v
X
-13-l-BR
H
R
I l l 1 't,jTFT
d J K L M
I
I
I
i
I
I
I
I
Volume 66
2'
Number 4
"
u
2
April 1989
2'
30 1
(16) The upper and lower pa* of the envelope are cut off along the lines VX and YZ', respectively. (17) On the reverse of the envelope, the points corresponding to T, W, P , Q, U, and Z are marked T*,W*, PL, Q*, V ,and Z*, respectively. Of course, the lines corresponding to ( K ) and (MI are marked (K*) and (Ma), respectively. (18) Obliquelines are drawn toshade the 10 triangles (TPW, WQX,
302
Journal of Chemical Education
PUZ, and QZZ'an the front, W W*, W*Q*X,P, U*Z*, and Q*Z*Z' on the hack, and T H P and HUU* on both sides). (19) The envelope is folded both backward and forward along the lines (K) (i.e., (K*)),(M)(i.e., (Me)), HR, T H (i.e., T'X), T P (i.e., T * P ) , WP(i.e., W*P"), WQ (i.e., W*Q*), X Q (i.e.,XQ*), UH (i.e., U*m, UP (i.e., U * P ) , Z P (i.e., Z*P;), ZQ (i.e., Z*Q*). and Z'Q (i.e., Z'Q*). (20) The right- and left-hand sides of the envelope are pushed together so that the five lines HP, PQ, QQ*, Q * P , and P H form a pentagon. (21) The five points U, Z, Z', Z*, and U* are brought together and are taped to produce the bottom of the model given in the title. The five shaded triangles (PUZ, QZZ', Q'Z'Z', PaU*Z*, and HUU*) are folded inside. (22) The five points T, W, X , W*, and T* are brought together and are taped to produce the upper part of the pentagonal pyramid desired. The five shaded triangles (TPW, WQX, XQ'W*, W*P*T., and THT*) are folded inside.
