William J. Sheppard The Columbus Laboratories
Battelle Memorial Institute Columbus, Ohio 43201
The Construction of Solid Tetrahedral and Octahederal Models
In teaching students about st,ereochc~nistry~ one frequently mentions tetrahedral and o c t i ~ l ~ r d ~arrangements al of groups about a central atom. Most students have had insufficient experience with tetrahedra and octahedra to appreciate what is implied in t,he conventional planar diagrams. I'or this reason it is desirable to have models for them to see and handle. Sturdy, solid models are more convenient, than hollow models made by taping together equilateral triangles. The method of making solid models presented here has the advantage that all saw cuts are in a plme perpendicular to one face or another of the block. Thus, models can be made easily with a band saw and miter box, or a band saw and miter gauge. A lest; attractive alternative is to make such models starting from a cube. To make an octahedn~n,one can rut of? all eight corners, using planes which bisect the three edges of the cube adjacent to each vertex. A tetrahedron can be made by cutting off four alternate corners by diagonal planes, each plane penetrating the three vertices adjacent to the vertex removed. In practice, however, it is very difficult t,o do t,his d h conrmtionnl shop tools.
Figure I . ~ C o n ~ t r u c t i r m of o tetrahedron.
Directions (See Figures 1 and 2) 1. Set the tahlo of l,he hand saw so that it is perpendicular to t,hr blade.
2. Lay out the st,ock as shown in drawing 1 of either figure. Note that the size is in the ratio 1 : 1: d1/2for the tetrahedron and 1 : 1: .\/i for [.he oet,ahedron. 3. Drill pilot holes 1.76 in. deep on each side where indicated hy t,he ci~cleson {.hedrawing. Make holes slightly emaller than the finishing nails (1.5 in. long) to be nsed. 110 not insert the nails a t this time.
4. Cut along lines m indicated in drawing 1. Save the scraps.
5. Reassemble pieces as shown in drawing 2 using the cardboard sheet,s to replace t,he sawdust removed (i.e., t o fill the kerf). (The cerdhoard should be the same thickness as the saw blade plus its set.) Drive finishing nails into the pilot holes and make them flush with a. nail set. A. Rotate the Mock 90' so that the nail heads are on the top and bottom. Cut along the lines as indicated in drawing 3.
7. The solid resulting is shown in drawing 4 of each figure. I t can now he painted on the vertices or sides to illustrate its symmetry propert,ies. Two solids can he connected hy dowel pins in such n way that they rotate to illust,~.ntethe existence of diaslelroisr~mors.
Figure 2.
Construction of on odahedron.
Volume 44, Number 7 I, November 1967
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