Stellated polyhedra – mathematical models

In the studio - stellated polyhedra with orange flower pillow

When I was about 12, my dad and I built four stellated polyhedra (star-shaped, many-sided platonic solids). Dad, a mathematician and math teacher, used the book shown below as a resource and then worked out his own dimensions and angles (you can see his notations right in the book). We hung the three largest polyhedra from the kitchen ceiling and they remained up there all the years I was growing up. I’m a bit heartbroken that I can’t find a photograph of them installed there. We simply hung them from cheap white cup hooks, using invisible dental floss which we knotted and glued inside the final glue joint of the model. This is what passes as decor in a math household, I guess. They were beautiful, colourful and modern, and kids and adults loved them. My friend Doug, who owns way more of these platonic solids than I do, recently said that he feels good just looking at them, and I know what he means.

Stellated polyhedron made with my father

The book Dad used, still one of the best resources for building geometric models, is Mathematical Models, 2nd Edn, by H. M. Cundy and A.P. Rollett, Oxford University Press, 1961. I am really surprised that you can’t find plans for these online, so that you don’t have to be a mathematician to make them. Has anyone ever found plans? Or perhaps kits? Dad and I made the models with only a geometry set, his calculations, mayfair cover stock, an X-acto knife, white glue, hand-mixed tempera poster paint (as they used to call it) and dental floss. I highly recommended this as a father-daughter project, not to mention as decor. A note on the colours: the faces aren’t painted randomly. The colours help you to see what’s going on in each model. In the model above, for example, each colour indicates a separate triangular pyramid – for a total of five intersecting pyramids. In the polyhedron in the far right of the top photo, each colour indicates either a star shape or a large triangle. The actual choice of colours, though, was subjective. Not surprisingly the polyhedron at top right is Dad’s colour scheme, while the girly one above was mine.

Mathematical Models

Mathematical Models

Mathematical Models

Mathematical Models - cover

Doesn't it make you want to sing and shout?
Cartoon we had on our fridge for years when I was growing up. You’d have to have known my father to know why this is so funny.

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8 Responses to “Stellated polyhedra – mathematical models”

  1. Eva Says:

    So beautiful! In one of the comments I read that they make you feel good by looking at them. I guess this is because they visualize the laws of nature. How about producing new ones? If industry did it (if it is not a sacrilege), they might be offered at a decent price and maybe sell like mad.

  2. John Hopper Says:

    Now that is really weird! I was sorting through my reference books this morning and I found the exact same book in amongst my stuff. It is a later paperback version, admittedly, but it’s the same book! I gave it back to my partner at lunchtime, and then a few hours later I read about the H M Cundy & A P Rollett book on your blog. Perhaps it’s a synchronicity event, but then again, maybe it’s just random events. Ah the beauty of science!

    My partner said that she used to make dodecahedron’s when she was a girl and hang them from her bedroom ceiling. Maybe making mathematical models is a girl thing!

  3. Anaka Narayanan Says:

    I love these! They look great (must be a lot of work to make them) and wish I could have a few for one of my photo-shoots to hang from the ceiling.

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  6. kerry Says:

    The college I attend is hosting this awesome conference next year. Looks like it will be right up your alley. Come to Baltimore!

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