Figure 8 Seifert Surface

by dennedesigns, published

Figure 8 Seifert Surface by dennedesigns Apr 1, 2016
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This is a Seifert surface of a figure 8 knot designed by Mithra Muthukrishnan and edited by Dave Pfaff and myself for my Math 341 Introduction to Topology class in Fall 2014. The colored model shows the knot in pink/red, one side of the Seifert surface in white and the other side in yellow

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You may need to rescale this object by a factor of 10 in Makerware since it is sized in cm not mm. You may also need to move the knot onto the platform, I think it is just above it. The knot is about 8cm x 8cm x 10cm in size. This knot was first printed on a Project 260 3D Systems printer.

How I Designed This

This was a complex design. The figure-8 knot and its Seifert surface was first created in SeifertView. After exporting the file, we opened it in Cinema4D. There the surface was extruded in both directions creating the two sides of the Seifert surface. Finally, three copies of the surface were made. In one, all the surfaces were deleted leaving the knot. In another the knot and one side of the extrusion was deleted. In the final copy, the knot and the other side of the extrusion was deleted. This left three pieces which could each be given their own color before printing. For the .stl file here, the model is just in one piece.

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The creator of SeifertView gave Washington & Lee University (my institution) a version of the program which enables you to export what you've created to a file. I would contact him directly and see if he can do something similar for you.

Hi, dennedesigns.

Quick Question:
I'm looking to create something similar to this inside SeifertView, and have finished my design. I'd like to export the model now, but can't find any option to save the 3D model. Would you mind pointing me in the right direction to export a 3D model from SeifertView?