Modeling a Dodecahedron
This is a 3d modeling tutorial for the platonic solid of dodecahedron. Modeling a dodecahedron is a good exercise for the basic transformation commands such as Rotate3D in Rhinoceros. You will see that it is possible to calculate the rotation angle by using sphere intersections. I learned this elegant method while teaching Architectural Geometry classes 12 years ago. It is based on the fact that, given a rotation axis and the rotation point, you can draw the path traced by that rotation. By observing the geometry of the dodecahedron, you can see that two such conditions must meet at the same point. Therefore, I show how to construct these two paths and intersect them to find the inner angle of this platonic solid.
These solids are very special because they also form the basis of many other complex solids and the geodesic spheres we use in architecture. It is important to know these modeling processes to comprehend the drawing as a form of visual calculation.
I studied this construction previously here. You can also see the step-by-step process of this construction in the previous post. The modeling and unrolling of a dodecahedron seem to be a very special case. However, the underpinning skills and visual thinking it requires are general and very valuable. It also encourages precision and the use of object snapping and three-dimensional control on the Rhino viewport. Combined, these skills are the fundamentals of CAD. From my experience, it is fair to say that, although the technology is so advanced in terms of AI and parametric modeling tools, etc., these basic drawing and precision skills of an architect are still missing and very valuable.
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