A completely different rendering of the cross-cap in 3 dimensional Euclidean space. This one is the image of the unit sphere about the origin under the map
(x,y,z) -> (yz,xz,xy)
Adam Coffman, who has a wonderful web page with pretty pictures and equations for Steiner surfaces , tells me that this is called Steiner's Roman Surface.
Just in case anyone's interested, here's the raw LDRAW .DAT file generated by my program.
Beware - the .DAT file builds it out of 1x1 bricks. Actually constructing this out of larger bricks so that it holds together is a (non-trivial) exercise for the reader! At the time of writing, this is easily the most difficult construction of all my Lego surfaces. In fact I had to cheat a bit and add some extra internal support for the nearly-horizontal bits near the middle of the model.
The pictures on this page are Copyright © A. Lipson 2000
Lego ® is a trademark of The Lego Group, who have nothing to do with this or any of my other Lego-related web pages.
My other Lego cross-cap sculpture
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Hits since 25 February 2002
This page last modified 2nd April 2005