http://www.google.com/search?q=Atommetrics&ie=UTF-8&oe=UTF-8 --"What would you call a circle with more than 360 degrees? Supercircles are our solution to a...
John Berglund <anisohedral@...> wrote: Hey Michael, Concerning the question of being "diatonic:" Pythagorus noticed that notes which have frequencies in...
... I doubt that the choice of western music to exclude ratios based on 7, 11 or 13 to one ratios is related to the fact that polytopes tend to not have many...
I was wondering if there were higher order polytopes with more than one axis of n-fold symmetry.My intuition now has changed - For example, an 8th dimensional...
John, I had to check more than once to make sure that you wrote this. Since when is John Berglund interested in the 'weird'? I am joking. You ask, from...
Alan, the email for Jerry Newport does not seem to work. Michael Donovan ... From: Alan Michelson To: Polytopia@yahoogroups.com Sent: Monday, December 06, 2004...
Some phylosophic In a universe with one particle only. There can not be time, or movement. In a universe with two particles only, then if the particles can...
In a message dated 12/6/2004 3:04:21 PM Central Standard Time, anisohedral@... writes: What kinds of symmetry exist in higher dimensions? In 4-D, the...
Hedrondude@...
Dec 14, 2004 11:00 pm
823
I don't understand this. Maybe my question wasn't clear. I am not looking for the combinations of symmetries. For example a cube has several planes of...
... I dunno much about any of this but here is something in crystalography I came across recently. I was spercifically trying to understand teh diffrrences...
I looked at how a tetrahedron can map its different vertices to itself. It seems that there are four ways: the identity, rotation (180 or 120°) around a line,...
Ah yes, http://www-history.mcs.st-and.ac.uk/~john/geometry/Lectures/L7.html This site came up with the same isometries, and gave a nice proof. It uses the term...
... In 4D, you can ROTATE any polychoron across or around a PLANE. In fact, you can rotate a polychoron around the W-X plane at the same time that you can...
... (That should be 120 of course :-)) ... Yes, the something weird is what I call rotation-reflection. Others call it rotary-reflection or glide reflection. ...
I see the pictures of symetry and as i am more graphicaly thinker then a math thinker. I remember images who looked quite in a certain way somehow Not realy...
... itself. It seems that there are four ways: the identity, rotation (180 or 1200) around a line, ... Ah, yes. instead of "ways" I should have called them...
Merry Christmas from me too :-) You can even buy the attached image on a Christmas card, although it's probably a bit late this year! You can also buy...
... Nope. There are infinitely many polyhedra, but they all have to belong to some symmetry group, and there aren't many different symmetry groups. They are...
I think that this page is missing more than the isosahedral symmetry groups. For instance it is missing the right regular prisms and antiprisms. It seems like...
... No, they're all here, although there are infinite series of some of them, which I forgot to mention. Each row except for the last represents an infinite...
... Ah, yes. I take it that C_n means that there is one n-fold rotation axe. C_nv have n (vertical on the pictures) planes of reflection that coincide in one...
... Yes, but one axis is an axis of course, not an axe. An axe is something you chop wood with :-) C = cyclic symmetry, ie like a pyramid. D = dihedral...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the Polytopia group. File : /priem.tif ...
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