Great Dodecahedron is a fascinating and mesmerizing polyhedron. It has 12 pentagonal faces( Can you guess the number of trianglular surfaces and whats unique about them?) . If you are interested to know more about the solid do check the following resources:
Acknowledgement:
I would like to thank Pranshi for helping during the process of making. This is an excellent activity to do in groups , takes very little resource to make and hopefully will inspire many to experience the beauty in the patterns!
Great dodecahedron is one of the Kepler-Poinsot polyhedra. Platonic solids are convex regular polyhedra but KP are non-convex. Great dodecahedran shares the same vertex and edge arrangement as that of icosahedron. This is yet another great resource to read more about these polyhedra http://www.georgehart.com/virtual-polyhedra/kepler-poinsot-info.html
This doesn’t directly answer the question, though, as to whether the Great Dodecahedron is a geometric transformation of a platonic solid.
On the ‘face’ of it, there certainly seems to be good reason to think that various (four, it appears) sets of convex surfaces have been inverted. But one of the conditions for a platonic solid is that all vertices be identical, which is not the case here.
Thinking further, however, it turns out that, after all, while a platonic solid has 3 affirming conditions, this does not apply to transformations of the sides of the solid, or to transformations of sets of sides of the solid.
So, the question is again open, I think. Is there some way of getting those triangular faces to be joined up such that they all meet in a convex shape, with each vertex being the meeting point of over 3 (but some fixed number) triangles?
