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Natural Science Forum / Physics / General Physics / May 2007Why no pentagon crystal lattices?
This question appears in the problem supplement to the Feynman Lectures: "Can you explain why there are no crystals which have the shape of a regular pentagon? (Triangles, squares, and hexagons are common in crystal forms.)" I can flail my hands about and say something like, 'there are no arrangements of pentagons which would result in a minimal energy configuration', but that seems like begging the question. Is there a geometrical explanation for this?  Signaturehttp://www.vho.org/GB/c/DC/gcgvcole.html http://www.vho.org/GB/Books/dth/ http://www.germarrudolf.com/ http://www.ice.gov/pi/news/newsreleases/articles/051115chicago.htm In sci.physics, hetware <massless@nutrino.none> wrote on Sun, 27 May 2007 11:21:53 -0400 <4vSdnZ6ZleaOP8TbnZ2dnUVZ_sKunZ2d@speakeasy.net>: > This question appears in the problem supplement to the Feynman > Lectures: "Can you explain why there are no crystals which have the shape [quoted text clipped - 5 lines] > configuration', but that seems like begging the question. Is there a > geometrical explanation for this? Well, one reason one doesn't see pentagonal crystals is a simple one: pentagons can't tesselate the plane. Hexagons, triangles, squares, rhomboids, and parallelograms, yes, but one can't fit together pentagons to cover an area. The best one can do is pentagons with certain gaps. Signature#191, ewill3@earthlink.net Useless C++ Programming Idea #1123133: void f(FILE * fptr, char *p) { fgets(p, sizeof(p), fptr); } -- Posted via a free Usenet account from http://www.teranews.com > In sci.physics, hetware > <massless@nutrino.none> [quoted text clipped - 15 lines] > triangles, squares, rhomboids, and parallelograms, yes, > but one can't fit together pentagons to cover an area. Though that may be a valid line of argument, it assumes that tesselating the plane is requisite. I don't deny that it is required, but one might speculate that crystals could form in some other way than arranged in a plane. I'm envisioning a bucky ball type of arrangement. > The best one can do is pentagons with certain gaps. There is another problem in the same set which I posted to sci.math earlier. What I learned from investigating it is that proving the obvious is not always easy. Have a look at the Kepler Conjecture. Here's my earlier post: "You are given a large number of steel balls of equal diameter d and a container of known volume V. Every dimension of the container is much greater than the diameter of a ball. What is the greatest number of balls that can be placed in the container?" My argument is this: The most efficient arrangement will be a lattice of tetrahedrons. The spheres in one layer will be arranged so that their centers form equilateral triangles with their neighbors. That means the distance between adjacent rows will be Sqrt[3] d/2. The spheres in the adjacent layer will be arranged over the centers of these triangles. Suppose these are the vertices of the first triangle in the first layer assuming d=1: v1 = {0, 0, 0}; v2 = {1, 0, 0}; v3 = {1/2, Sqrt[3]/2, 0}; To find the fourth vertex in the tetrahedron, we first find the center of the triangle: vc=(v1+v2+v3)/3={1/2, 1/(2 Sqrt[3]), 0} Then we find the vertical displacement that will result in an edge of unit length. vc.vc + z z= 1 z z=1-1/3 z=Sqrt[2/3] v4={1/2, 1/(2 Sqrt[3]), Sqrt[2/3] } We really didn't need v4 to solve the problem, but it helps in understanding it. What we now have is the fact that there are X/d spheres in a row, there are Y/(d Sqrt[3]/2) rows in a layer, and there are Z/(d Sqrt[2/3]) layers in a volume XYZ. n = Sqrt[2] XYZ/(d^3) Does that look right? Signaturehttp://www.vho.org/GB/c/DC/gcgvcole.html http://www.vho.org/GB/Books/dth/ http://www.germarrudolf.com/ http://www.ice.gov/pi/news/newsreleases/articles/051115chicago.htm In sci.physics, hetware <massless@nutrino.none> wrote on Mon, 28 May 2007 04:01:06 -0400 <q72dnXxDJZLXEcfbnZ2dneKdnZydnZ2d@speakeasy.net>: >> In sci.physics, hetware >> <massless@nutrino.none> [quoted text clipped - 20 lines] > speculate that crystals could form in some other way than arranged in a > plane. I'm envisioning a bucky ball type of arrangement. Buckyballs are dodecahedrons; they don't tile space too well. :-) In fact, the only things that *do* tile space offhand are parallelpipeds and a combination of a tetrahedron and an octahedron. One could of course combine dodecahedrons with something else; I'm not sure what that something else would be, but it would fill in the gaps. But that doesn't mean dodecahedrons tile space. >> The best one can do is pentagons with certain gaps. > [quoted text clipped - 42 lines] > > Does that look right? Well, now you've shifted gears on me, but the sphere-packing problem is a known one, and AFAIK has been solved, with great difficulty. The best ratio possible is pi/(3 * sqrt(2)) =~ 0.7405: http://mathworld.wolfram.com/SpherePacking.html http://www.sciencenews.org/pages/sn_arc98/8_15_98/fob7.htm Signature#191, ewill3@earthlink.net fortune: not found -- Posted via a free Usenet account from http://www.teranews.com On May 28, 4:41 pm, The Ghost In The Machine <e...@sirius.tg00suus7038.net> wrote: > In sci.physics, hetware > <massl...@nutrino.none> [quoted text clipped - 98 lines] > > - Show quoted text - ------------- had the Atom or nucleus been spheres *th e **number of possible combinations structures of those Atoms * (of heavier than Fluorine ) would be*** much bigger **!!! only a tetraheder shape of the heavier than fluorins can explain why th enumber of possible 3d structures are as is the key question that experts should ask themselves is why is the number of combination structures is 'so limited ' !!! and than you will get just one hint about the real structues of single Nucs and Atoms Y.Porat ------------------ On May 27, 7:40 pm, The Ghost In The Machine <e...@sirius.tg00suus7038.net> wrote: > In sci.physics, hetware > <massl...@nutrino.none> [quoted text clipped - 26 lines] > -- > Posted via a free Usenet account fromhttp://www.teranews.com --------- that is not the comprehensive answer the better answer is actually one of the verifications of my nuclear and Atomic model elements until Fluorine are composed of Alpha particles that are tetraheders above fluorine it becomes 'rectangular pipes' or more accurate it is sort of octahedr pipe but from bonds point of view it is a rectangular pipes that basic structure gives unequivocally the hexagonal 3d structures the interesting thing is tha this nuclear structure goes fron Fluorine upwards all the way to the heaviest elements so i suggest that you consult expert No 1 of nuclear and Atomic structure ie one that has as for now the best closest to reality model see just the appetiser of my model in www.geocities.com/porat_y/mypage.html (prodided i typed it without mistakes from my memory (:-) ATB Y.Porat --------------------- [...] How nice - a reason that totally denies analytic geometry. > [...] > > How nice - a reason that totally denies analytic geometry. ------------- imbecil crook and hand waiver moron jsut piss of and mind your parroting bissiness it is apparent that you are a disturbed personal enemy and a walkind damage to the advance of science but it whant help you !! go finish first your BSC !! and only than you wil become....... a real beginner parrrot !! (:-) Y.Porat ------------------- [...] That's OK - geometry is hard. It is much easier to make up some sh.t theory instead. > [...] > > That's OK - geometry is hard. It is much easier to make up some sh.t > theory instead. -------------- imbecil Nazi bump parasite crook!! and disturbed moron as well that diverst posts to his moron ng and ddint notice untill now that it does not work on me (he is not intelligent enough to notice even that (:-) why cant there be a planar ring of a heavy Atoms of say 20 Atoms in each ring or even mor ethan 8 ?? while each one of them is spherical ?? that question is not for the disturbed undergarduate Shaise Y.Porat ------------------ > imbecil Nazi bump parasite crook!! > and disturbed moron as well [quoted text clipped - 10 lines] > > that question is not for the disturbed undergarduate Shaise Froth. Foam. Froth. Foam. Rinse Repeat. SignatureCOOSN-174-07-82116: Official Science Team mascot and alt.astronomy's favourite poster (from a survey taken of the saucerhead high command). Official maintainer of the supra-cosmic space fluid pump (Mon and Tues only). > > imbecil Nazi bump parasite crook!! > > and disturbed moron as well [quoted text clipped - 16 lines] > > Repeat. Y. Porat, Always delete alt.usenet.kooks off your responses to Gay-Tard Phineass T. PuddlePuss or you'll have a dozen AUKers attacking you! You don't want that! Good day, HJ In sci.physics, Y.Porat <y.y.porat@gmail.com> wrote on 28 May 2007 01:27:46 -0700 <1180340866.504103.79660@w5g2000hsg.googlegroups.com>: > On May 27, 7:40 pm, The Ghost In The Machine > <e...@sirius.tg00suus7038.net> wrote: [quoted text clipped - 39 lines] > > Alpha particles that are tetraheders Um...Alpha particles are buried deep in the nucleus, if they can indeed be conceptually isolated at all. Apart from the positive charge protons do not partake at all in chemical reactions, and neutrons just add mass. If you are referring to the probability structures of various electron orbitals, they do indeed form various odd looking structures (at highly minute dimensions, of course, which means we conceptually have to "zoom in"; the size of an atom is about 250x-500x smaller than visible light). However, none of them are pentagonal. > above fluorine it becomes > [quoted text clipped - 14 lines] > one that has as for now > the best closest to reality model And the reason I would need a nuclear expert to explain chemical considerations such as crystallography is ... ? > see > just the appetiser of my model in [quoted text clipped - 3 lines] > (prodided i typed it without mistakes > from my memory (:-) Considering your atrocious diction, I'm not hopeful. :-P You can't even spell "Linus Pauling" or "abstract" correctly. The accompanying PDF is badly typeset, though Table 2 is of some interest, but with no explanation on how the values were calculated. (Ideally, the Standard Model would have a similar table. Of course observed values should be reasonably readily available.) One of the more interesting claims; UNDERSTAND MY CLAIM- THAT IN HEAVY NUCLEI: THE NUMBER OF ELECTRONS AROUND THE NUC IS NOT NECESSARILY THE NUMBER OF PROTONS IN THAT NUC!. [sic] The diagrams look like a combination of bacteria and Tinker-toys. This doesn't necessarily make them wrong, but they're certainly not standard. > ATB > Y.Porat > --------------------- Signature#191, ewill3@earthlink.net Linux. The choice of a GNU generation. Windows. The choice of a bunch of people who like very weird behavior on a regular basis, random crashes, and "extend, embrace, and extinguish". -- Posted via a free Usenet account from http://www.teranews.com On May 29, 2:25 am, The Ghost In The Machine <e...@sirius.tg00suus7038.net> wrote: > In sci.physics, Y.Porat > <y.y.po...@gmail.com> > wrote > expert No 1 of nuclear and Atomic structure > > ie > > one that has as for now [quoted text clipped - 44 lines] > > - Show quoted text - ----------- thank you Ghost btw sorry i dont know your ereal name it could be muchnicer now i satrt o repect you as a serious scientist tha tbothered to spend a minima time on my model now i wonder why you pick on me say on myspelling of say paulling instead of Pauling i was dwelling on the opening page more or less as i dwell now on my post (:-0 i was in stress i didnt know how to handle all that site bui,ding and it took me a few minutes to 'sjape that opening page' includiong the confution of not knowing how to insert a link etc etc in short i am a cpmplete igorant in sit ebuilding and eevn to this moment i dont know how toedit that page and fix a silly mistake like spelling Pauling i had his book and lerened a lot form him about the geometric structure of the Atom even later i realise that in some parts he was not adavnced enough !1 at themoment i was scribbling the openiong page i didnt have the book on my front so i jsut typed Pauling from mwemory without thinking twice so he goes the 'Pauk\ling' that all 'experts' that rad it see it as a n indivcation of my model !! (:-) whileactually understand nothing about the invaluable real sunstance of the model fo rme it is a good indication about hoe much they dont understand it and just spewing now to your undersyatnding it: you cant in a few moments we deal with a quite bu tnot 'in heaven' 3d structure most mathematics parrots are completely untrained even as a structural engineer todeal with 3d structures now it becomes more difficult while youi ahve to express it on a flat paper can you immasgine a structure like see the lead nuc ) drawn on a flat paper while you have to describe ther dozens of detailes that are lying in 3d ??!! so i had to invent a sort of a codish system of graphyisc laguage todoit simper on a paper and let mr tell you that without that graphic invention i had no changeto deal withthose structures even while iam atrained structuralenginer becaie waht you see is klus tthe bottom line of my work btw jsust a few of the 92 that i solved and you should knowe that i did a long many years about a thousand of trial and error structues untill it was satisfacrory from mass chemistry cristalline and other knwn data to fit it to one harmony !! yes sindeed my beginning was walking in copplete darkness of trial end errors but gradually i satted to find that there is some law and oeder in it which i defined unequivocally and amde my work easyer as tome went on i dont reveal all thsose laws in my absrat because of secrecy reasone! no one is entitled according to my interets toknow anything about my model so amy be it is one of the reasons peole dont find their hand and legs there it is just an apetiser for peole that *i* will chose to know it all laong and probably could advance it further but only after realy knowing it that has to take months of study !! ie only for serious *responsible* people 2 you are rigth one of my surprising and difficult to get even for me at eh beginning was the revolusinaly finding that The number of electrons 'arounf the nuc' in a heavy atom is not neccessary the number of Porotons init enough for today (:-) ps sorry for not spellcheking even me can see a lot of mistakes.. yet one still can understand me with some effort 3 think abou tmy question who for insatnce not more than 6 Atoms in a 'ring' of 'alleged 'spheres ' !! ATB Y.Porat -------- In sci.physics, Y.Porat <y.y.porat@gmail.com> wrote on 28 May 2007 20:32:50 -0700 <1180409570.231061.299900@w5g2000hsg.googlegroups.com>: > On May 29, 2:25 am, The Ghost In The Machine > <e...@sirius.tg00suus7038.net> wrote: [quoted text clipped - 57 lines] > it could be muchnicer > now i satrt o repect you as a serious scientist I'm no scientist, just one of the laymen. :-) > tha tbothered to spend a minima time on my model > now i wonder why you pick on me say on myspelling > of say paulling instead of Pauling I'm a professional nitpicker, admittedly. :-) (My job is to develop programs, which involves debugging.) > i was dwelling on the opening page > more or less as i dwell now on my post (:-0 [quoted text clipped - 84 lines] > in a heavy atom > is not neccessary the number of Porotons init You'll have to some some good evidence for that one. It is, of course, possible to ionize any atom -- with the possible exception of hydrogen, for there's only one electron, and even then, it is possible, though one ends up with a slightly odd compound (H3OH+, I think) rather than a naked proton. There are also strange issues with the metallic bond. I'd frankly have to look at this point; presumably, some of these issues lead to things such as thermocouples. However, in an atom's more or less natural state, the charges should match. > enough for today (:-) > [quoted text clipped - 7 lines] > who for insatnce not more than 6 Atoms > in a 'ring' of 'alleged 'spheres ' !! There are 12 atoms in the closepackings I'm aware of. Several variants are possible but I'd have to look; the general idea is to have sheets of regular hexagons overlapping one another. At each hexagonal vertex is a sphere of the requisite radius. > ATB > Y.Porat > -------- Signature#191, ewill3@earthlink.net Useless C++ Programming Idea #40490127: for(;;) ; -- Posted via a free Usenet account from http://www.teranews.com On May 29, 8:57 am, The Ghost In The Machine <e...@sirius.tg00suus7038.net> wrote: > In sci.physics, Y.Porat > <y.y.po...@gmail.com> [quoted text clipped - 209 lines] > > - Show quoted text - -------------- you saied that th enumber of positive charges ahs to be as the negative ones very nice !! yet did it ever occure to you that many Protons that are deep in the nuc .... lost their positive charge while they made the strong inner bonds ??!! 2 as you say the base for all heavy Atoms is Alpha particles that are tetraheders NOTHING ELSE !! some of them has additional protons neutrons deuterons at their perifery but the main skeleton of the heavy nuc is ALOHA PARTICLES that are tetrahedrons ! ANDNOT SPHERES you can enclose an Alpha by an IMMAGINARY SPHERE yet it is not a sphere!! bacasue a real sphere has matter all over its envelope while the tetraheder does not it has electron 'arms' just in certain directions therefore the number of directions in which it can make connections is limited!! and that is why th enumber of structures it cam make *is less than expected form a sphere !! ATB Y.Porat ---------------- Look up sulfur chains and rings. Heck, look up cycloparaffins. In sci.physics, Autymn D. C. <lysdexia@sbcglobal.net> wrote on 29 May 2007 18:15:03 -0700 <1180487703.852910.125360@n15g2000prd.googlegroups.com>: > Look up sulfur chains and rings. Heck, look up cycloparaffins. Benzene. :-) Signature#191, ewill3@earthlink.net Linux. Because it's not the desktop that's important, it's the ability to DO something with it. -- Posted via a free Usenet account from http://www.teranews.com On May 30, 9:42 am, The Ghost In The Machine <e...@sirius.tg00suus7038.net> wrote: > In sci.physics, Autymn D. C. > <lysde...@sbcglobal.net> [quoted text clipped - 14 lines] > -- > Posted via a free Usenet account fromhttp://www.teranews.com ---------- as far as i know benzen is the clasical discovery of kekule it is a hexagon but not a palanar one it is 'in two sories' ie 3d now biological compouns are a stor for itself the y are far complicated to folow all its detailes ie for insatnce 'how many 'stories' (leveles) each of them has !! my question is in a **single plan** !! to make it simpler and to make a point !!! ATB Y.Porat ----------------- In sci.physics, Y.Porat <y.y.porat@gmail.com> wrote on 29 May 2007 00:41:55 -0700 <1180424515.263969.27580@p77g2000hsh.googlegroups.com>: > On May 29, 8:57 am, The Ghost In The Machine > <e...@sirius.tg00suus7038.net> wrote: [quoted text clipped - 221 lines] > lost their positive charge > while they made the strong inner bonds ??!! And this is documented precisely where? A proton is two ups and a down; a neutron two downs and an up. Gluons can shuttle between quarks, but charge is conserved no matter what they do, unless an electron wanders in (electron capture) -- and charge is still conserved, since the electron gets essentially eaten, cancelling one of the positive charges. > 2 > as you say > the base for all heavy Atoms is Alpha particles > that are tetraheders NOTHING ELSE !! Oh, now you're being a tad ridiculous. The basis for all heavy atoms is the same as the light ones: protons and neutrons, or, if you prefer, up and down quarks. > some of them has additional protons neutrons > deuterons at their perifery > but the main skeleton of the heavy nuc is > ALOHA PARTICLES that are tetrahedrons ! I'll admit to wondering. Of course, the alpha particle as traditionally represented is a fat tetrahedron, (two balls placed across two other balls) but that's not an accurate representation any more than a clay model of an automobile is a car. The Bohr model was discarded long ago for electrons; the same should be done for the nucleus, though I frankly don't know what the result should look like other than it's all fuzzy and contains a certain number of up quarks, a number of down quarks, and a lot of gluons. The best I can do is that there are 6 up and 6 down quarks in an alpha particle. This may partially explain why so many radioactive atoms eject alpha particles, as opposed to single protons or neutrons. (Some do eject beta particles, admittedly.) > ANDNOT SPHERES > you can enclose an Alpha by an IMMAGINARY [quoted text clipped - 5 lines] > it has electron 'arms' just in certain > directions Don't be ridiculous. The electrons are way outside of the nucleus. > therefore the number of directions in which > it can make connections is limited!! [quoted text clipped - 5 lines] > Y.Porat > ---------------- Signature#191, ewill3@earthlink.net Linux. Because it's not the desktop that's important, it's the ability to DO something with it. -- Posted via a free Usenet account from http://www.teranews.com On May 30, 9:42 am, The Ghost In The Machine <e...@sirius.tg00suus7038.net> wrote: > In sci.physics, Y.Porat > <y.y.po...@gmail.com> [quoted text clipped - 69 lines] > -- > Posted via a free Usenet account fromhttp://www.teranews.com ---------- Hey Ghost you have a looooooooooot to learn!! (:-) you are not even a beginner about nuclear and Atomic structure anyway i can promise you it is a whole wondeful like 'new continent' to dsicover !!! to explain it to you about your satte of knowlwdge lets take a methaphore: supose one would ask you about Americal and you would anwer oh !! yess !! i heared rumours that ....... that America is far away in the west and may be if you sail west you migh tfind land but it is not sure because you might fall into the end of the world ] and it is probably India ..... and if you land there may be you will find there yelow people with an ancient culture and i think that thiet capital city is New Delhi!! and i cant recall or immagine anything more about America !! (;-) that is more or less your situation with nuclear and Atomic structure anyway if you ahve free time i tmigh tbe a wonderful(endless !!) adventure fo ryou to find better knowledge ...... ATB Y.Porat --------------------- In sci.physics, Y.Porat <y.y.porat@gmail.com> wrote on 30 May 2007 02:37:06 -0700 <1180517826.601570.57600@u30g2000hsc.googlegroups.com>: > On May 30, 9:42 am, The Ghost In The Machine > <e...@sirius.tg00suus7038.net> wrote: [quoted text clipped - 76 lines] > > you have a looooooooooot to learn!! (:-) I freely acknowledge that, admittedly. Of course I do know the basics, and know where to find certain information -- e.g., halflife decay rates for isotopes. > you are not even a beginner about > nuclear and Atomic structure anyway [quoted text clipped - 14 lines] > but it is not sure > because you might fall into the end of the world The original discovery of America was misattributed to India; hence the term "Indian" for what we now call Native Americans. >] > and it is probably India ..... [quoted text clipped - 10 lines] > i tmigh tbe a wonderful(endless !!) adventure fo ryou > to find better knowledge ...... Yeah, well without predictive formulae to accompany your structures, how on earth are they useful? Your affairs remind me of the "Smart Model", with the oxygen atom showing up light a doughnut in his theory. Admittedly, from a philosophical standpoint I would wish for better methods than shooting at atoms with the atomic equivalent of nuclear bombs (well, come to think of it, the atoms *are* part of atomic bombs)...but that's the best we can do, and the debris can be quite interesting, and is routinely analyzed. > ATB > Y.Porat > --------------------- Signature#191, ewill3@earthlink.net Linux sucks efficiently, but Windows just blows around a lot of hot air and vapor. -- Posted via a free Usenet account from http://www.teranews.com > This question appears in the problem supplement to the Feynman > Lectures: "Can you explain why there are no crystals which have the shape [quoted text clipped - 5 lines] > configuration', but that seems like begging the question. Is there a > geometrical explanation for this? Ghost has given you the correct answer. > --http://www.vho.org/GB/c/DC/gcgvcole.htmlhttp://www.vho.org/GB/Books/dth/http://w ww.germarrudolf.com/http://www.ice.gov/pi/news/newsreleases/articles/051115chica go.htm In sci.physics, Eric Gisse <jowr.pi@gmail.com> wrote on 27 May 2007 13:58:55 -0700 <1180299535.063771.170210@q19g2000prn.googlegroups.com>: >> This question appears in the problem supplement to the Feynman >> Lectures: "Can you explain why there are no crystals which have the shape [quoted text clipped - 9 lines] > >> --http://www.vho.org/GB/c/DC/gcgvcole.htmlhttp://www.vho.org/GB/Books/dth/http://w ww.germarrudolf.com/http://www.ice.gov/pi/news/newsreleases/articles/051115chica go.htm There are, however, some interesting planar coverings if one is not required to use a single shape. The pentagon can tesselate if it uses a rhombus in concert, for example; a heptagon can tesselate with a pentagon, though the latter is not quite regular. Of course one can also cheat in a number of ways, by assembling shapes in a tesselable geometry (box, triangle, hexagon) and repeating it; one can even get creative and randomly rotate the shapes in some cases. http://education.ti.com/educationportal/activityexchange/download_file.jsp?cid=U S&fileurl=Math%2FGeometry%2F4600%2FGeoInvestigations_Voyage_Cabri_Act06.pdf I'll admit I'm not sure why a pentagonal crystal cannot fabricate itself from a seed, though (presumably that has to do with atomic bonds and/or basic chemistry), but if one assumes a grid of such seed crystals, there would have to be gaps. Signature#191, ewill3@earthlink.net Windows. Because it's not a question of if. It's a question of when. -- Posted via a free Usenet account from http://www.teranews.com > This question appears in the problem supplement to the Feynman > Lectures: "Can you explain why there are no crystals which have the shape [quoted text clipped - 5 lines] > configuration', but that seems like begging the question. Is there a > geometrical explanation for this? Quasicrystals. Aperiodic lattices can diffract sharp spots with 10-fold symmetry. The lattices are periodic in 5-D, then are projected to 3-D. http://www.geom.uiuc.edu/apps/quasitiler/ SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 [snop river of sh.t] |
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