An easily constructed Dodecahedron model

An Easily Constructed Dodecahedron Model Shukichi Yamana Faculty of Generali Education, Kinki University, Kowakae, Higashi Osaka 577, Japan t ' 7n \ ror) { VX 4 m Db Q | N tee) 4 ' r a m T b ' \ oF --p---------- o : i2] m a Pp OR -- --— - —- eee Kee b falls on the horizontal! line DF, and its corresponding point is marked as L. 12) The upper part of the envelope is unfolded. 13) The upper part of the envelope is folded down at J so that the K falls on the other horizontal line EG and its corresponding point is marked as M. 14) The upper part of the envelope is unfolded. 15) The lower part of the envelope is folded up along the line DF. The point on the left-hand side of the envelope corresponding to J is marked as N, and the point on the original front of the envelope corresponding to M is marked as O. Thus, a regular pentagon OLMN4 is obtained. 16) The lower part of the envelope is unfolded. Thus, a regular pentagon OLMN- is obtained. 17 All diagonal lines of this regular pentagon are drawn, and all intersections obtained are marked as P, Q, R, S, and T, respectively. 18) All diagonal lines of the small regular pentagon PQRST are drawn and all intersections of their extensions with the five sides of the large regular pentagon OLMN/J are marked as ], 2,3, 4,5, 6,7, 8, 9, and 10, respectively, as shown in the figure. 19) The intersection of the extension of the line 83 and the left- (or right-)hand side of the envelope is marked as U (or V). 20) The corresponding points on the reverse of the envelope, of the three points L, O, and P, are marked as L*, O*, and P”, respectively. 21) The envelope is turned upside down. Now, the original back of the envelope becomes the new front. 22) The upper part of the envelope is folded down along the line VU’, and the corresponding points on the new front of the envelope, of the three points L*, O*, and J, are marked as L*’, O°’, and J’, respectively. Now, a new regular pentagon P*7J’O*’L*’, is obtained. 1 | 23) AU diagonal lines of the regular pentagon P*7J‘O*’L*’, are drawn and all intersections obtained, are marked as R*, 6*, W, M*, and X, respectively, as shown in the figure. } 24) Al diagonal lines of the small | reguiar pentagon R*6*WM*X, i are drawn and all intersections of their extensions and the five | sides of the large regular pentagon P*7J’O*’L*', are i} 1 Ternansky, Robert J., Balogh, Douglas W. and Paquette, Leo A., J. Amer. Chem. Soc., 104, 4503 { 1982). 1)) The upper part of the envelope is folded down at J so that the K T 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 at A so that the line AB falls on the left-hand side of the envelope. The points on the left-hand side of the envelope corresponding to points B and C are marked as D and E, respectively. The new corner on the right-hand side of the envelope is marked as F. 3) The lower part of the envelope is unfolded. 4) A horizontal line, perpendicular to the left-hand side of the envelope at E, is drawn so that it crosses the right-hand side of the envelope at G. 5) The lower part of the envelope is folded up at A so that the line AG falls on the left-hand side of the envelope and the corresponding point of the G is marked as H. 6) The lower part of the envelope is unfolded. 7) The lower part of the envelope is folded up along the line DF. The point on the left-hand side of the envelope corresponding to E is marked as I, . 8) The lower part of the envelope is unfolded. 9) The middie point on the line JH is marked as J. 10) A horizontal line perpendicular to the left-hand side of the envelope at J is drawn so that it crosses the right-hand side of the envelope at K. VaAdy — A mode! of a dodecahedron which is necessary for teaching stereochemistry (for example, that of dodecahedrane CopHo)! can be made easily by using a sealed, empty envelope. The steps are illustrated in the figure and given below. SSa & TRAMANDA,S. 8 marked as I], 12, 13, 14, 3*, 15, 16, S*, N, and 17, respectively, as shown in the figure. 25) Separate the front and back of the left part of the envelope from each other by cutting the 6 tt 1058 Journal of Chemical Education 27) Oblique lines are drawn to shade ten equilateral triangles . UP2, 3Q@4, 5R6, 7S8, and : 9770, on the right moiety; and I J6R*S*, and N6*17 on the left moiety). H1W12, 13M*14, 3*X15, 9°S g “ Ww for) ~ J left-hand side and the base AB of the envelope along their lines. Unfold the whole envelope.

28) Nine congruent equilateral triangles are drawn and painted black oD aie eerie ! Er --'y-x mzoe. i to cover the nine outer sides (S*7, P*16, P*15, L*’3*, L*’14, O*'13, O*'12, J’11, and J’7) of the five small regular pentagons on the left moiety. 29) Cut off the blank paper along the outlines of the figure. 30) Cut the remaining portion along the lines (JP, 3Q,5R, 7S, and 9T, on the right moiety and 77 W’, 13M*, 3*X, 16R*, and N6*, on the jeft moiety). 31) The remaining portion is folded both backward and forward along all the sides of all the smal! regular pentagons. 32) The five outer corners of the regular pentagon OLMNd, are forced to approach each other so that the five lines 1P, 3Q,5R, 7S, and 9T, fall on the other five lines 2P, 4Q, 6R, 8S, and 10T, respectively, and the shaded triangles (7P2, 3Q4,5R6, 7S8, and 9T 10) are folded inside. The sides are taped together to form the right half of the dodecahedron. oOo - 1 zn p> ! i ,M 8 zcwm™ C = ~) Oo Zz cm A 1 33) Similar procedures are applied to the other regular pentagons on the left moiety. In this step, the five lines 1] W, 13M*, 3*X, 16R*, and N6*, fal] on the other five lines 12W, 14M*, 15X, S*R*, and 6*17, respectively. The sides are taped together to form the left half of the dodecahedron. 34) The left and right halves are forced to approach each other so that the nine outer edges of the right moiety (8/, J9, 100, 01, 2L, L3, 4M, M5, and 6N) fall on the other nine outer edges of the left moiety (7S*, 16P*, P*15, 3*L*°,L*'14, 130*’, O*'12, 11d’, and J’17), respectively, infolding all the black triangles inside. The sides are taped together to produce the dodecahedron. An Earty Account of the Unhappy Consequences of Unauthorized Experiments Those in charge of student laboratories have continually sought to discourage students from conducting unauthorized experiments. Here is an early, perhaps the earliest, account of such an unauthorized experiment and the consequences thereof. This account clearly indicates several important points. It shows that unauthorized experimentation has long been disapproved and by an authority even higher than many deans. It further illustrates the dire consequences that can result from such activities. “And Nadab and Abihvu, the sons of Aaron, took each of them his censer, and put fire therein, and laid incense thereon, and offered strange fire before the Lord, which He had not commanded them. [Emphasis mine.] And there came forth fire from before the Lord, and devoured them, and they died before the Lord.” (Leviticus 10:1,2) Benjamin Ruekberg Lyndon State Coltege Lyndonville, VT 05851 Volume 61 Number 12 December 1984