Tutorial: Exploring the Platonic solids in 3D max

Among the many discoveries of Plato, an ancient Greek mathematician and philosopher, were the mathematical formulas that defined perfect geometric solids. A perfect geometric solid is one that is made up of polygon faces that are consistent throughout the object. The five solids that meet these criteria have come to be known as the Platonic solids.

Using Max, you can create and explore these interesting geometric shapes. Each of these shapes is available as a primitive object using the Hedra primitive object. The Hedra primi- tive object is one of the Extended Primitives. To create the five Platonic solids as primitive objects, follow these steps:

1. Open the Create panel, click the Geometry category button, and select Extended Primitives from the subcategory drop-down list. Click the Hedra button to enter Hedra creation mode, or select the Create➪Extended Primitives➪Hedra menu command.

2. Click in the Top viewport, and drag to the left to create a simple Tetrahedron object. After the object is created, you can adjust its settings by altering the settings in the Parameters rollout.

3. Select the Tetra option in the Parameters rollout, set the P value in the Family Parameters section to 1.0, and enter a value of 50 for the Radius. Be sure to press the Enter key after entering a value to update the object. Enter the name Tetrahedron in the Object Name field.

4. Click and drag again in the Top viewport to create another hedra object. In the Parameters rollout, select the Cube/Octa option, and enter a value of 1.0 in the Family Parameter’s P field and a value of 50 in the Radius field. Name this object Octagon.

5. Drag in the Top viewport to create another object. The Cube/Octa option is still selected. Enter a value of 1.0 in the Family Parameter’s Q field this time, and set the Radius to 50. Name this object Cube.

6. Drag in the Top viewport again to create the fourth hedra object. In the Parameters roll- out, select the Dodec/Icos option, enter a value of 1.0 in the P field, and set the Radius value to 50. Name the object Icosahedron.

7. Drag in the Top viewport to create the final object. With the Dodec/Icos option set, enter 1.0 for the Q value, and set the Radius to 50. Name this object Dodecahedron.

8. To get a good look at the objects, click the Perspective viewport, press the Zoom Extents button, and maximize the viewport by clicking the Min/Max Toggle (or press Alt+W) in the lower-right corner of the window.

Figure 6-8 shows the five perfect solid primitive objects. Using the Modify panel, you can return to these objects and change their parameters to learn the relationships between them. Later in this chapter, you can read about the Hedra primitive in greater detail.

platonic-solids-in-3d max

Figure 6-8: The octagon, cube, tetrahedron, icosahedron, and dodecahedron objects; Plato would be amazed.

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