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Old 09-14-2021, 07:34 AM
Laurence Finston Laurence Finston is offline
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Polyhedron models: Small Rhombicosidodecahedron


I have just finished plans for a paper or cardboard model of a Small Rhombicosidodecahedron:

The webpage is here: The GNU 3DLDF Polyhedron Models Page
There are other, older models on this page as well. i believe the last time I worked on them was 2011.

General instructions are here:

The net is from the book Mathematical Models by H.M. Cundy and A.P. Rollett, 2nd edition, Oxford University Press, 1961, p. 111. I'm not sure whether it's in print or not; I think probably not.

It's been one of my favorite books ever since I discovered it by chance at the library as a child. After having checked it out many times over the years, I finally found it for sale at a used book store.

Since there is no text on this model, generating the plans in different sizes is no problem. There is a single parameter that governs the size of the model of the polyhedron itself, namely the radius of the surrounding circle of the pentagon. For the tabs, there are a couple of parameters governing the size, shape and placement, but it would easy to adjust them for different sizes of the model.

There are some extra tabs which will need to be cut off. This shouldn't be a problem. In a couple of places, I wasn't quite sure which were needed and which weren't. It's better to have too many than too few. However, if any are missing, a piece of paper can be used as a substitute; strictly speaking, they're just a convenience.

I chose approximately the largest size for which the plans for the entire model can be printed on a single DIN A3 piece of paper.

There are interesting ways of coloring the faces of polyhedra in order to bring out the various kinds of symmetry present, depending on the polyhedron. Unfortunately, I've never gone further into this than finding some references which I no longer remember. In addition, it's been a long time since I've worked on this material and I need to brush up my geometry.

I have one book in German which goes into this topic: Farbige Parkette by K. Bongartz, D. Mertens, W. Borho and A. Steins. "Farbige" or "farbig" means "colored" and "Parkette" are tessellations or tilings of the plane and polyhedra are closely related to tessellations. However, I doubt very much if this book is in print and it's probably not as widely available as Cundy and Rollett.

If I learn a good way of coloring the present model I will update the plans on the website, as I will do for any other additions or corrections.

Any feedback would be much appreciated.

Laurence Finston
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mathematical models, polyhedra, polyhedron

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