Because The LEGO Company get paranoid about this sort of thing I suppose I'd better make it clear that I have no formal affiliation with them, that my views are my own and do not necessarily represent theirs, and so on. So if you think any of this is official you are as deluded as they are.
A cross-cap is what you get when you glue every point on the boundary of a disk to the point exactly opposite it. This is a bit hard to do in just three dimensions, so the resulting surface self-intersects along a line...
Like the Mobius band , a cross-cap is a one-sided surface (in fact, another way to construct one is to glue the circular edge of a Mobius band to the circular edge of a disk).
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!
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 25th February 2002
This page last modified 1st April 2005