## Sunday, December 7, 2014

### Zinnia Star

Zinnia Star, by Meenakshi Mukerji

I made this model as a gift for a friend of mine who is a teacher.  After it was completed, it occurred to me that it would collapse under the weight of all the children in her classroom, so I did the forbidden and added some glue.  It was quite sturdy afterwards!

The shape here is a great stellated dodecahedron.  I thought that was odd at first, because I look at it and I see triangles.  There are 20 triangular pyramids in the model.  Dodecahedron = 12 pentagons, and icosahedron = 20 triangles.  So why is it called a stellated dodecahedron rather than an icosahedron?

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect.
To stellate a dodecahedron, you need to extend out each of its planes.  If you extend them out, you can get progressively larger stellations (right column of images from Wolfram):

It's neat to rotate around this figure and try to imagine the tiny dodecahedron inside.  Although I already gave the model away...

#### 1 comment:

miller said...

This is beautiful.