## 2-dimensional symmetry on 764?

Case number: | 671071-995809 |

Topic: | Game: Other |

Opened by: | BootsMcGraw |

Status: | Open |

Type: | Question |

Opened on: | Friday, August 23, 2013 - 23:07 |

Last modified: | Saturday, August 31, 2013 - 02:45 |

The five-fold symmetry of puzzle 764 appears to be only in one plane, along an imaginary X-Y axis drawn through all five chains.

This strikes me as odd. Things pack more tightly in three dimensions than in two. Wouldn't polymers be symmetric in all three dimensions? For example, four points are equidistant along the surface of a sphere when they are oriented like a tetrahedron / pyramid. I would think that five points, and therefore, five chains would also try to end up equidistant along the surface of a sphere, although I don't know what that shape would be called.

Dev's: Is this intentional? Or is the game programming not sophisticated enough to handle symmetry in 3-D?

Actually, there is something close: the trigonal bipyramid.

https://en.wikipedia.org/wiki/Trigonal_bipyramid_molecular_geometry

I was thinking that pentamers would try to align according to trigonal bipyramidal geometry.

Five-sided donuts are boring.

Yes, puzzle 764 has C5 symmetry. We think of it as having 5-fold rotational symmetry about the Z-axis, which gives rise to "planar" designs.

And you're right, there are certainly other types of symmetry in known proteins than the simple C-group symmetries. However, there is also a surprising amount of simple rotational symmetry in nature (for a C5 example, see nicotinic acetylcholine receptors).

Aside from the "dimer of dimer" puzzles, like Puzzle 636, Foldit symmetry puzzles have all had simple rotational symmetry. We've stuck with rotational symmetry simply because it's a little easier to think about during design, and also because it's compatible with single-chain puzzles. There will certainly be future puzzles with more complex symmetries (personally, I'm pretty excited about these).

As an aside, five is kind of a funny number here, because there is not (to my knowledge) any other way to position 5 equidistant points on the surface of a sphere.