Zometoll models for the stellations of the dodecahedron
Here we describe how to build the stellations of the dodecahedron, one of the five regular polytopes in 3-dimensional space, using the zometool system. For the model you need
- 112 balls,
- 90 long blue (b2) struts,
- 120 modele blue (b1) struts,
- 30 short blue (b0) struts.
The pictures below were taken by Eva-Maria Gassner.
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First Stellation
The small stellated dodecahedron
Using b1-struts, 12 pyramids are erected over each of the pentagonal faces of a b0-dodecahedron.
Second Stellation
The great dodecahedron, which is one of the Kepler-Poinsot polytopes
To obtain the great dodecahedron from the small stellated dodecahedron constructed above, one connects (using b2 struts) the tops of the pentagonal pyramids. The outer shell is an icosahedron.
Third Stellation
The great stellated dodecahedron
To obtain the great stellated dodecahedron one starts with an icosahedron and erects a pyramid with a triangular basis over the each of faces (each edge of such a pyramid consists of a b0 and a b1 strut). The drawback is that the original dodecahedron is not visible in this model and that some of the balls do not represent vertices.
The final model
This is the final model and shows all three stellations of the dodecahedron at the same time. The innermost polytope is a dodecahedron, the second shell is a small stellated dodecahedron, the third shell shows the great dodecahedron and to outer shape is the great stellated dodecahedron.