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enter image description hereenter image description hereMy daughter is in the first grade, and I'm having a good deal of fun trying to determine the shapes of irregular geometric solids. I'm stuck on the good, old beanbag. enter image description here

Here are the parameters.

  1. Theoretically, it's a rectangular prism, a cuboid of sorts.
  2. But when I sewed it (it was originally two 2-dimensional pieces of cloth, and turned it inside out it became not square but octagonal (b/c we didn't push out the edges all the way).
  3. Then we filled it (with beans), and it makes a hexagonal pillow shape as seen in the pictures.
  4. I'm working on trying to determine the correct nomenclature for, using things things like lists of polyhedra, but the "roundness" of the bag, its "convex elongated"? quality makes me wonder what, really, is is. http://en.wikipedia.org/wiki/List_of_uniform_polyhedra
  5. Essentially, it's like giving a name to a kind of pillow. I tried to post photos here but was unable to...

Any thoughts are most helpful! Thanks, Julie

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Try to fix the link to your image and maybe someone might be able to give an answer. –  Samuel Reid Jan 11 '12 at 4:17
You shouldn't delete the [1]: http://i.stack.imgur.com/XXXXX.png line that gets automatically added when you insert your picture. It's how the website knows where to find the image. –  Rahul Jan 11 '12 at 4:22
Without a picture it's hard to say. However, I've seen bean bag patterns in which you take a pair of square pieces of fabric then sew the edges together such that each of the 4 straight edges of the first piece get sewn to the two half edges surrounding a vertex on the second piece. This would produce an octagonal profile like you say. Adding folds between the midpoints of the edges on each square piece, it will be in the shape of a Square antiprism. en.wikipedia.org/wiki/Square_antiprism –  Adam Jan 11 '12 at 7:05

1 Answer 1

I found this paper which calls it a "square pillow" (section 6.2). Because of the rounded corners one might call it a "truncated square pillow" by analogy to polyhedra nomenclature. The paper seems to be about polyhedra inflated with (mathematical) air rather than stuffed with beans, but the images on page 11 look very similar, aside from the corners. Note that the "square pillow" is not a polyhedron. A polyhedron that I think resembles this shape is the square orthobicupola.

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