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Hey,
Awesome post! Larry has a point with the text on the studs, but when I teach
symmetry and chirality and talk about everyday objects I always put in the
caveat “this baseball has such-and-such symmetry properties, igoring all
imperfections and this text over here”.
Which, of course, leads to an expansion on Didier’s original post, you can
describe the symmetry properties and point groups of each brick. For instance,
a 2x4 brick has two planes of symmetry (that is, you can divide it in half
either between two 2x2 fragments or between two 1x4 fragments and the two halves
are mirror images of eachother) and a C2 axis (that is, you can rotate it 180
degrees along an axes parallel to the direction of the studs and get the same
thing), so it is in the C2V point group. A 2x2 brick is in the C4V point group.
A 2x2x1 slope is Cs, and so forth.
A stack of bricks is sort of like a crystal structure, with a repeated pattern
of unit cells. It turns out that molecules of certain point groups will fit
into certain types of crystal lattices, while others will not. Or sometimes
chiral molecules will fit into certain crystal lattices only when paired with
their enantiomers. In the same way certain bricks will stack to form certain
types of repeated structures, whereas others will not, or perhaps certain forms
will work if you pair up chiral bricks with their enantiomers etc.
Speaking of repeated patterns, I found
this from Brickfest to
be an interesting demonstration of this.
Bruce
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| LEGO and chirality Chirality is the property of an object that can not be superimposed on its mirror image. Examples includes both natural (biological) object such hands and cultural (technical) object such screws. A non-chiral (achiral) object can (...) (19 years ago, 8-Sep-05, to lugnet.build.schleim, lugnet.parts) !
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