Suggested models

We will use this post to collect ideas and suggestions of things to print.  See also the Project List page to see which projects already have people working on them.

  • Prof. Rasmussen:

    Given any knot, one can find a polynomial parametrization of said knot, and as a result, it can be represented as the vanishing set of some ideal of polynomials in R^3. As a result, each individual polynomial in the ideal describes a surface in R^3 that contains the knot. This gives a beautiful visualization that I think 3-d printing could provide.

    I would love to have any of the following:

    (a) a surface in R^3, with a highlighted copy of the knot embedded in it, (or even the same for several different surfaces),

    (b) two different colored surfaces in R^3, (whose intersection would be the knot in question).-1

    • Prof. Emeritus Linton suggests the Steinmetz surface as a nice, symmetrical surface.
    • Prof. Ramyaa has some ideas about 3D printing a demonstration of how a 3D model can be reconstructed from several 2D images.
    • Prof Constantine would like models illustrating the Hopf fibration.250px-Hopf_Fibration

    I would also like to print models of the Sierpinski pyramid and the Menger sponge.

  • Prof. Scowcroft suggests we look into the series of models Felix Klein popularized at the Chicago World’s Fair.
  • We should certainly print some cubic surfaces with their 27 lines:clebsch

Borromean_Seifert_surface

  • A pseudosphere illustrating some of the principles of non-Euclidean geometry.pseudosphere
  • Some minimal surfaces, including the helicoid and catenoid:Helicatenoid
  • Prof. Pollack suggests printing some models of lattices in R^3 which have interesting connections to algebra.
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