Tetrahedron and the Related Cube

With the printed side of the template downward, fold along all the solid lines after folding each of the flaps, push it flat again. 

Molecular Symmetry David J. Willock 2009 John Wiley Sons, Ltd. ISBN 978-0 70-85347-4 

Cut out the triangular areas marked Remove using a sharp craft knife it may help to place a ruler next to each line as the cut is made. Push out each triangle, taking care not to crease the remaining paper in the model. 

Apply glue to each of the flaps and glue them under the side with the corresponding number indicated on the template. Flap 1 is to be glued in place first flaps 2, 3 and 4 should then be glued together. One side of the cube is left open, and so pressure can be applied to these flaps from inside the box shape formed. 

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The tetrahedron is an important shape in chemistry. Methane, the complex [Ni(CO)4] and many other molecules in which a central atom has four equivalent bonds take on this geometry. The symmetry of the tetrahedron is best discussed with reference to a solid model, and a paper template is provided in Appendix 3 from which a tetrahedron and the related cube can be constructed. This paper model also has some representative symmetry elements drawn on it which are also illustrated in Figure 3.25. The highest order axes are C3 which join each corner of the tetrahedron to the centre of the opposite face. There are four corners, and so there are four axes each gives rise to two operations (C3 and Ci ), and so 8C3 appears in the title line of the character table (Figure 3.26a). 

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