Saturday, February 18, 2012


The following discussion was entered into between myself (Bobhexa) and other members of

This was my endevour to see if there was a congruence of shared geometry.

Bobhexa (Quark) 06-06-2007, 02:14 AM
Capsid Geometry
I recently googled "AIDS" and "Cancer" and stumbled across a site that was dated 2005 which stated that a common ancestor billions of year ago allowed the DNA in viruses to evolve and that it uses the the same basic protein "fold" to construct the critical outer shell. I question this common ancestor theory insofar that billions of years ago the existing forces at that time are the same kind of forces we experience today.A sphere is formed because of these forces . Would it be more acceptable to saythat geometry is the language of these forces?
Location: Hawaii, Oahu, Manoa Valley

foodchain (Organism) 06-06-2007, 10:49 AM
Much of ancestry in terms of biology can also simply be viewed via genetics and what not. As for you idea of geometry playing a role in some way or ways I don’t see why not. Life is based on the physiochemical like most anything else, be it a solar system of the geology of earth.
Join Date: Jan 2007 Posts: 1,126 Location: earth

bobhexa (Quark) 06-06-2007, 01:14 PM
Thanks Foodchain for your response.My reason for asking the original question is that I have discovered a new flexible construction element which can be formed into a sphere which appears to look like a capsid kind of geometry.
Location: Hawaii, Oahu, Manoa Valley

foodchain (Organism) 06-06-2007, 02:27 PM
I cant view the link. No big deal, I am somewhat interested in what you are talking about though. Reading stuff from say biophysics they are heavy on structure as its more readily able to accept being put in mathematical forms, such as the crystal lattice and what not.
Location: earth

CharonY (Biology Expert) 06-06-2007, 03:02 PM

To be honest, I do not quite get what you mean. Viral capsules usually build themselves via self-assembly. This means that the information of how to assemble themselves is already provided by the proteins which constitute these capsules themselves. The authors you cite (Fokine et al; btw it is easier if you provide links btw ) have noted that tailed phages (in particular T4 and HK97) share a similar structure in the capsule, which they share with some eukaryotic viruses. So similar structures (and also assume conserved domains) hint that dsDNA containing phages might share a common ancestor.
It has long been recognized that 3D structure is conserved over much longer timespans than nucleotide or amino acid sequences (42). Thus, the large number of structural and functional similarities of tailed phage capsids makes it probable that these and the capsids of other related viruses have diverged from a common ancestral source. Considering the high abundance of phages on Earth (43), the HK97 capsid fold must be one of the most frequently occurring structures in the Earth's biomass.
Thus I do not understand your reasoning, as phage capsids are complex structures (as proteins go) and are not random molecules "pressed together" by some geometrical forces, as it might be interpreted from your post (at least I did). Change the amino acid sequence and you won't obtain a capsule.Judging from the link that you have given the patent is about the construction plans for a macroscopic construction unit. I fail to see the connection except for rough similarities. Like, say comparing golf balls to apples.

bobhexa (Quark) 08-12-2007, 04:32 PM
Well I have been trying to put my ideas into a more logical order. I fully grasp the facts of viral self assembly. The question I have is what influenced the amino acid sequence? It appears that each variety of capsid geometry design has an equal matching twin in the material world of crystals. CharonY, you mention the phrase common ancestral source….Does the word “ancestral” preclude the crystal as having had any relevance in the design of proteins? If so, then what is the source of the geometry that they both share?What is the common source more likely to be? Do ambient forces acting upon matter dictate how things will form?. Couldn’t these forces that cause a crystal to grow in a certain manner also act upon proteins? They both start from “nothing” and expand into being. So what came first? Was it a photo finish? A strange freak of coincidence!Imagine blowing a steady stream of air through a narrow straw into a bowl of soapy water....blow enough bubbles to create three levels/layers/tiers.Observe middle layer .....what do you see??The link between this subject and my patent is that when I construct a double skinned sphere from this material it offers a brand new geometry for study that emulates certain capsids double skinned appearance.

bobhexa (Quark) 06-06-2007, 03:13 PM
Ty ,Yes, I take your point FoodchainIf you register (takes 2 minutes) you will be able to view the link.Please give it a try. Good luck
Location: Hawaii, Oahu, Manoa Valley

bobhexa (Quark) 06-06-2007, 07:15 PM
Thank you Charony for your well considered response.Yes, it’s all in the interpretation and you may have jumped to the wrong conclusion. No, I do not think that capsids are formed from random molecules “pressed together” by geometrical forces. The C60 molecule is a truncated icosahedron and it would appear that most capsids appear to take this geometry. Do you know the exact geometry of these family of capsids?If you do not then I am offering you a possible geometry to research. All in the name of knowledge. This maybe the last precept to form another concept.You fail to see the connection except for rough similarities. Like, say comparing golf balls to apples.So, like, say comparing C60's and capsids. Are they that far apart?
Location: Hawaii, Oahu, Manoa Valley

foodchain (Organism) 06-06-2007, 08:07 PM
C60, that’s a buckyball right I don’t know the chemical composition of the item in question fully but I don’t think its based on C60. If you are more or less speaking in terms of the forces that give C60 its shape is the same in regards to what gives the item in question its shape, I don’t know to what extent that would be true as I have never giving it much thought/study. Its an interesting association, but on that note I don’t know how much the impact a structures geometry has in regards to interactions in the first place, such as a square making square waves when dropped in a liquid for instance, probably easier for circle I would imagine. I also do not understand fully of course the reality of chemical bonds in regards to molecular shape and fully what such derives from. Such as Carbon being able to exist in various configurations, such as diamond or graphite; More so in a case by case basis. I would think that reaction mechanisms have environmental variables involved, which could I guess play into it on some level, but overall I don’t really think I understand enough your question overall. If per say its just structure, well structure is important in biological systems, and is also conserved as I think was already pointed out.
Location: earth

CharonY (Biology Expert) 06-07-2007, 01:17 AM
No, I do not think that capsids are formed from random molecules “pressed together” by geometrical forces.The C60 molecule is a truncated icosahedron and it would appear that most capsids appear to take this geometry. Do you know the exact geometry of these family of capsids?
I think you are completely on the wrong boat. See, a C60 simply consists of, well carbon. Capsids however are proteins, a far more complex composition. Check the original paper in which the crystal structure is resolved. The geometry of the phage heads is thus governed by the amino acid sequence. There are other viruses that have different architectures (e.g. retroviruses) which thus likely do not share the same common ancestors as T4 and related phages. Comparing an evolved protein structure with fullerens, even if they should share geometrical similarities is like assuming that there must be a common force between tennis balls and oranges.You are confusing very different things here.
Last edited by CharonY; 06-07-2007 at 06:00 AM.

bobhexa (Quark) 08-21-2007, 12:31 AM
Moving on
Okay, I accept that, based upon the lack of replies from my posting of the image that it does not interest you bio-engineer guys. That is okay as I had originally posted that this exercise is for the sake of getting the concept out into the knowledge bank as I really do consider that this geometry has some important application somewhere in engineering. I tried you guys first! It must exist somewhere in nature ...perhaps it is a foolhardy belief of mine that if something is elegant and efficient that it will have already been utilised by Mother Nature. Perhaps I am naive.... Nanoworld next stop....medical stent perhaps.
Location: Hawaii, Oahu, Manoa Valley

pioneer (Molecule) 08-30-2007, 02:14 PM
In crystals, the final geometry is not only impacted by the binding forces between atoms, but also due to external factors such as the solvant composition, foreign atoms, or even something simple like cooling profile. Typically one of the crystal shapes is minimum energy, while others may still be stable but contain some potential relative to the minimum potential shape. For example, if you took steel and hit it in one place with a hammer, this will affect the crystals at the point of impact and add potential. This will often be the first place to rust because of the potential that was added. Relative to C, diamond is the most stable crystal form of C. The capsid, by looking at it, looks cool, but it appears to indicate stored potential. This could be useful if one wished to build something stable, that contains a little extra potential so it can be used as a type of catalyst. Or it may allow stable electron states that are a little higher in energy than normal.Addressing viral self assembly, the potential in the water will put the squeeze on anything that tries to increase its potential. At the same time, the viral components have binding areas that allow these to minimize their own energy. Between the push of the water and the pull of the binding areas they self assemble. It does its best to minimize potential under the circumstances. But again, like the capsid, minimum potential is relative. Potential can be stored into a stable configuration. This makes it easier, later on, for the virus to shed its protein shell and release the DNA.
Location: Mandarin, Florida

bobhexa (Quark) 09-06-2007, 11:31 PM
With capsid in hand............
A very interesting viewpoint Pioneer You say that “ Potential can be stored into a stable configuration. This makes it easier, later on, for the virus to shed its protein shell and release the DNA.” Consider then, could it be that the concertina geometry of this sphere is ‘stored potential’?When internal pushes come to a shove, the double skinned sphere will gradually expand outward into a single skinned angular truncated icosahedron.During this process of expansion the 12 pentagonal openings get larger in diameter. Could this be an unknown mechanism allowing it to ‘shed its protein shell and release the DNA’Do either of the views(last post), in any way or form, appear capsoidal? If it were so, it would need to be in an immature state of development, prior to shedding.

Location: Hawaii, Oahu, Manoa Valley

bobhexa (Quark) 06-07-2007, 05:59 PM
I think we are getting hung up on the subject of forces.I am trying to draw your attention to the fact that there are exact similarities between space fillers and capsids. Suppose that I have discovered a new kind of geometry which goes a step beyond a truncated icosahedron by making it double skinned. This would be a geometry which has not as yet been discovered.Would it be of any interest at all to your profession? page 11 of 14 Coxsackie virus based on the truncated icosahedron
Location: Hawaii, Oahu, Manoa Valley

foodchain (Organism) 06-07-2007, 07:07 PM
I have to say that’s a really interesting reading for anybody interested. Secondly, what is your primary interest for the study of such? Is it more leaning towards evolution per say, or more towards structural geometry period? If its for evolution, there is a broad range of stuff that’s already known that I think would take sometime to integrate into that paper(you produced?).If its purely for structural purposes, well then I guess one would have to take into account on some level if the chemistry life typically uses, or that of what you study actually permits in some level of exactness what you are stating, as put forward as a possible tool in the paper for evolution for instance. Which structure of life is conserved such as having X limbs, or two eyes for instance. The problem I get is where the evolution thing ties into what works in the ecology overall in regards to any variables, such as needing to run, and how needing to run impacts the body. My guess is all that as you would have it structure and geometry play some role along with various forces and the chemical structures and so on, or available chemistries and I don’t know of any living things with some organic titanium joints for instance. Well anyways, please feel free to post more in reply, I find that very interesting.
Location: earth

CharonY (Biology Expert) 06-08-2007, 02:35 AM
Hmm maybe I understand a bit better what you mean now (but then, maybe not ;P)I assume that may main problem with your reasoning and my focus in forces vs. structure is this from your OP:
which stated that a common ancestor billions of year ago allowed the DNA in viruses to evolve and that it uses the the same basic protein "fold" to construct the critical outer shell.I question this common ancestor theory insofar that billions of years ago the existing forces at that time are the same kind of forces we experience today.A sphere is formed because of these forces . Would it be more acceptable to saythat geometry is the language of these forces?
These sentences consists of a number of different assumptions that, at least to me do not sum up. Therefore I will try to ignore what I assume to be inconsistencies and try harder to get what you mean (yeh, I am probably thick-headed).Anyway, what I do not understand yet is what you mean with geometry? Do you mean structure? And do you mean identifying given structures in nature or about creating them, as e.g. in nanotechlogical applications? Or are you more interested mathematical modeling of said structures? Anyway, I still got to read the pdf first, when I got more time. Will get back to you then.
Last edited by CharonY; 06-08-2007 at 02:45 AM.

Bluenoise (Biology Expert) 06-08-2007, 03:43 PM
He's basically making a comparison of the structural of viral capsids to various geometries. Like dodecahedrons etc... Along with this is the use of two different mathimatical methods to generate these geometries. Either the use of simple mathametics or a quantum harmonic ocillator.A fairly interesting read actually. Lot of great images.Though the math is definatley a little past what I've become accustomed to.
Location: Canada

bobhexa (Quark) 06-08-2007, 07:16 PM
CharonY……Well, I must say that I admire your tenacity for staying with the thread, a subtle thread at that! Foodchain….your’e an angel sent to smooth rough edges (600 grit or more)Blue noise…. Ta very much for either the summing up of me or of the author of the link, I wasn’t quite sure to whom you were referring. However you do a fine summing up with a shrewd burst of objectivity.Okay I insist that you all really make an effort to log on to the original patent site link go to Figure 13 on page 7 of 14in the patent. There you will find a line drawing of a spherical structure .The line photograph was made from a halftone photograph of a sphere which I built using the construction element that I have discovered. I say ‘discovered’ because it is has always been there in the geometrical world but amazingly unnoticed by “Acadamia”. It is pure geometry without the interference of humans. I just followed the geometry.There is an undiscovered family of tiling units that can also take on this folding attribute in 3D geometry….namely… equilateral triangle, square and hexagon. I want you guys to take note of it and see if it has an application to your work! . The different surface areas they present seem akin to 3D geometry and a perfect fit in capsid structure. Perhaps we can look upon capsids as 3d geometrical structures and who really cares as to how they came to be, whether it was harmonics, mathematics, waves or geometry but just the fact that they ‘are’.
Location: Hawaii, Oahu, Manoa Valley

bobhexa (Quark) 06-08-2007, 09:05 PM
This is a sweet site also I refer you to page 5 of 9I rather like the phrase "Mechanism of formation"
Location: Hawaii, Oahu, Manoa Valley

Sphere Packing

bobhexa 11-26-2007, 09:18 PM
Sphere packingAs a geometist I remain intrigued by the attached diagram which I drew a long while ago. I endevoured to draw eight circles around a larger circle so that all the circumferences touched. By rough measurement it appeared that the ratio of the diameters of the smaller circles to the diameter of the larger centre circle was very close to the Golden Section.A good friend and mathematician advised me that it was close but no coconuts were to be won.Well I have since wondered about the fact that it was so close. I have expanded my wondering to go 3 dimensional and to consider spheres instead of circles. So the question is gentlemen would spheres which are manufactured to have their diameters exactly a golden section ratio of the central sphere be able to pack around this central sphere and make an exact fit.
Location: Hawaii, Oahu, Manoa Valley

Bignose (Maths Expert) 11-27-2007, 01:33 PM
The closest packing circles of equal radius can have is . The closest packing spheres can have is . You might really like the article "Cannonballs and Honeycombs" by Hales in Notices of the AMS, vol 47, 2000, because it has a neat discussion of these issues and other shapes being close packed.
Location: Iowa

bobhexa (Quark) 11-28-2007, 02:25 AM
I thoroughly enjoyed your reference to Thomas Hales .'Tis a very good informative piece of work. Absorbing reading.I gradually understood that he was talking mainly about similar sized circles or similar sized spheres.My , I think, bottom line question is as follows. Supposing that you have a single sphere of 100 mm diameter and you have a plurality of smaller spheres with a diameter of only 62 mm (Golden Section ratio).....are you able to to distribute the smaller spheres around the surface area of the larger sphere and maintain perfect contacts between all neighbouring spheres. Is it a perfect fit?Having pondered this, I am led to the conclusion that a c60 pattern is the answer.You guys are the mathematicians. Do the ratios of the diameters of the larger sphere and the diameter of the 20 smaller spheres come anywhere close to the golden section ratio?
If you think you can do a thing or think you can't do a thing, you're right. -Henry Ford
Location: Hawaii, Oahu, Manoa Valley

bobhexa (Quark) 12-09-2007, 02:35 PM
Up to my eyeballs.

My attached diagram doesn't seem to be valid so I shall upload the image again. Using the C60 Buckyball as a reference, I joined 20 polystyrene foam balls together with toothpicks. In other words each of the twenty hexagons of the C60 were replaced with spheres.Surprisingly the overall appearance is of a pentagonal dodecahedron. Could it be that the truncated icosahedron can also be described as a truncated pentagonal dodecahedron?Could somebody please work out the math as to what the diameter of the inner sphere might be if the smaller surrounding spheres had a diameter of 100mm.Thanks in anticipation.
Location: Hawaii, Oahu, Manoa Valley

bobhexa (Quark) 12-20-2007, 07:35 AM
In the interim I have built a large model of a buckyball and obtained fairly precise measurements of the internal diameter...that is from the centres of the diametrically opposed hexagons.It would seem that the ratio of the diameter of the hexagon(flat to flat)to the inner sphere is certainly in the ballpark of the golden section. It is within hundredths of an inch.I am still wrestling with a method to calculate this mathematically.Any ideas Gentlemen.Mele Kalikimaka to all.
Location: Hawaii, Oahu, Manoa Valley

bobhexa (Quark) 12-29-2007, 04:22 PM
In order to clarify I made up this model of 20 foam balls. They coincidentally fitted perfectly into this buckyball framework toy. Question....What would be the diameter of a sphere that fitted perfectly inside this model if the smaller surrounding spheres had a diameter of 100mm?
Location: Hawaii, Oahu, Manoa Valley

bobhexa (Quark) 03-29-2008, 11:26 PM
Nobody seems to have applied their brains to this question
Is my description too ambiguous or is this a really difficult computation.I would be so grateful if somebody would please try to calculate this out. Aloha Bobhexa
Location: Hawaii, Oahu, Manoa Valley

cjohnso0 (Quark) 04-12-2008, 07:04 AM
Well, on first try I came up with an maximum inner sphere size of ~180.2517mm.Basic methodology was as follows, refer to this page (Figures 2 and 2A) took the 100mm sphere diameter and set this equal to the length of one of the dodecahedron sides. Using this, you can find the length of the sides of the cube which fits perfectly into the dodecahedron.I came up with cube side length of 50/cos 72.Next, I figured that the tetrahedron inside the cube would have the closest packed 4 spheres. So I found the length of it's sides, which came out to be 50*sqrt(2)/cos72.Using this, the radius of a sphere circumscribing the tetrahedron is r=sqrt(6)/4 * Side Length.Subtract 2 times the radius of the balls, or 100mm and I got my answer.Final equation was (hopefully)D = 2*(50*2*sqrt(3))/(4*cos 72) - 100which was ~180.2517Let me know if my method is way to confusing to read. Not that I'm 100% sure I'm even close....
Location: Western Mass.

bobhexa (Quark) 04-13-2008, 07:04 PM
Getting closer
Dear cjohnso0Hi Aloha and thank you for your reply. The Kenneth MacLean site is a golden referral...I must buy his book.I was with you all the way through to the finding the length of the side of the cube. It was at that point I got lost but I realised that the diagonal of that cube coincides with the diametrically opposed spheres of my model dodecahedron.(see earlier Attachment) And then as you say subtract from this diagonal length twice the radius of the balls, or 100mm . Does that give us the same answer?Thanks again
Location: Hawaii, Oahu, Manoa Valley.

Three Dimensional Tiling

It is only the regular hexagon, the square and the equilateral triangle that can perfectly "tile the plane".
In the adjacent picture the left column shows a simple geometric arrangement of 7 hexagons combined with 9 squares.

The middle column  shows a simple geometric arrangement of 21 squares (9 combined with 12).

The right column shows a simple geometric arrangement of 6 triangles combined with 6 squares.
A progression can be seen building from top to bottom as they move through their simple stages of growth from zero to single layer, to double layer and finally to three layers.

This demonstrates that the three basic geometric tiling elements of the two dimensional plane can be used as building blocks toward three dimensionality.

When a collection of any one of these three elements are combined with a collection of  squares it results in a set of three repeating geometrical tiling patterns.
These three patterning , when folded at the boundary lines between the squares and the other chosen element, in a concertina fashion, will allow the  two dimensional pattern to become a three dimensional structure.
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