More than a year has passed since I successfully completed, with a great deal of help from the forum, my 3v Icosahedron model.
I am now considering making the 4v form ... but will again need help with the dihedral angles.
I have the cord factor and angles for all the individual triangles .... quoted in Borin Van Loon's book 'Geodesic Domes' but do really need some help with the all important dihedral angles.
Can anybody help me please?
I did wonder if you had gone on holiday.... I have not started on this project yet ...... just gathering up information and bits and bobs.
I am actually very, very busy on another massive project ....I am writing my dissertation for an MA. (Indian Literature)
But I do like to clear my head by working on these wood working projects.
Wow..... that looks great!
Let me play around a little with these figures and I will get back to you.
Off the top of my head..... this, in practice, boils down to only three angles 7.8 degrees, 10.0 degrees and 10.37 degrees. (the difference between 10.36 and 10.38)
One possible method of testing these figures, fairly quickly, may be to make just one section in this manner and the remaining 19 'faces' from sheet MDF. The 'joint' will not be exactly correct but, I feel, at this point in time, it should be a good guide.
Making an Icosahedron from MDF sheet is quite an easy option and if I join the MDF faces together with dowels then .... I hope that I can replace individual MDF solid faces with 4V format faces and, if things are looking good, gradually build the full 4V in this manner.
DO YOU THINK THIS METHODOLOGY WILL WORK?
Yes, The thinking was quite correct.
The only angle that I needed (except, of course, constructing the triangles) was setting the bandsaw to 21.7degrees. This angle was used to construct the pyramids and the dodecahedron that the pyramids sit onto.
Just messing about with the design for the base which will contain the microwave turntable drive motor and the wiring for the blue and white LEDs.
When I skin the shape with small triangles of mirror acrylic it should look quite different.
The base ......My thinking at the moment is a triangular pyramid with base of say 8 inches sides and the height of the apex about 2.25 inches...... a very quick drawing of this shape seems to fit quite nicely with the shape of the 'stellation'.
I should be able to work out the chord lengths and the dihedral.
An interesting shot show the construction of the small stellation of a dodecahedron.
The Pentagonal pyramids are all attached to a central Dodecehedron core.
Note the faces of the pyramid have been rebated to take the 'skin'.
I will make a base to house the drive motor and will construct in a similar manner but think I will make the base in the form of a pyramid but with an angle that corresponds to the angle that the tripod legs make with the base.
Need to work this all out.
Thinking about the 4V project ....
This afternoon I decided to map out the 4V form onto the 'rough' model of a Icosahedron that I made when I was working on the 3V form.
When I made the 3V .... after producing all the individual triangles I sub-assembled the pentagons and hexagons prior to full assembly.
Looking at this model the above procedure will not work.... in my opinion.
What I will probably do is sub-assemble the 12 pentagons and sub-assemble the remaining 13 triangles that constitute a 'face'
Just thinking about it at the moment.
It is going to be a few weeks before I can start this new project so no rush.
But I do like to plan everything in advance.
Working out how much timber I need.
What I am going to skin it with
Arranging the motor drive
And, above all, the 'Dihedral Angles' or the way that I cut them using these figures.
I would love to go ahead with the 4V form.
But honestly the maths is more than a little beyond me.
I understood everything (from a practical point of view) that you so kindly worked out for me for the 3V and I believe that the photograph that I posted is more than proof that your maths was spot on..... I was very impressed with your working methods.
I am presently constructing the small stelation of the dodecahedron which I believe will look quite stunning .... I am actually 'skinning' it with mirror acrylic and incorporating a LED light show in the base...... When this is finished I would love to construct something a little more difficult.
The 4V form... If I made every individual triangle based on B = 2 inches (from the Icosahedral symetry network that I posted about two days ago) then I estimate that I would end up with a sphere some 20 inches in diameter..... I think I can get this through the workshop door.....
When I was working on the 3V form I made myself a working drawing based on your figures (which I will post shortly)
If you would so kindly provide me with the set of figures, from which I could construct a similar working drawing, I would be very appreciative.
Anything is possible!..... sure angles can be cut with hand tools to the degree of acuracy needed but if you consider that the 3V form of the Icosahedron is made up from some 180 triangles each consisting (in my method of construction)) of three pieces of wood . These individual components are mitred at each end and one face angled..... this adds up to a lot of individual joints.
I would equate this task as similar to 'fashioning a grand piano from jelly with chopsticks'.
Re-reading your posting..... the north & south poles could not be placed at the top or bottom of other columns..... the picture would not match up. The individual pieces of the network need to stay firmly attached to their buddies. However, as I explained above, the whole thing can be pivoted as required.
Hope this helps!
You will need 'Photoshop' to sort of 'host' the filter .... It may work with the cut down version of Photoshop called 'elements' but I have not experimented with it.
The top of the 2nd column is normally the Nouth Pole and the bottom of the 3rd column is the South Pole.
However, you can arrange them differently like having the 'star' (top of the 9th column) as the North Pole and shuffling everything about.... but I can tell you from experience that this is quite a mind blowing excercise...... the best approach is to assemble, as presented in the net, starting at the North Pole then placing the matching pieces together like a jigsaw. Then, with some system of numbering, shuffle them around the 'sphere'.
Another way is to assemble the pictures before deciding which are the 'Poles'.
Another problem, which I experienced doing 'Babushka', was that I had a hexagonal face as N & S.
The 'net' always places a pentagon at N & S
I could not figure how to cope with this so started again.... I had to make another pentagon face to acommodate the rotational spindle.
In Flexify 2 you can select any of 20 forms of input and filter them to 80 types of output.... lots of combinations! The output for this was 'football' or something like that..... all the usual sorts of mathematical shapes are listed
Just type 'Flexify 2' into 'Google' and follow the links.
The white tabs are designed so that you could construct this model from paper and glue it all together..... I ignore them but put the photograph onto layers.... print onto 6x4 photographic paper..... laminate to protect the print .... then cut them out and stick them onto the model with doubles sided tape.... meaning I can quite easily change the photgraph when I should wish to.
If one selects the distorted bits and place them at say the North Pole.... they look quite good.... I rotate the whole thing with a micro-wave turntable motor.
The way to do this is to use a 'filter' in conjunction with Adobe Photoshop called Flexify2. This filter is quite amazing... One needs to purchase it but it is not expensive.
Some parts of the photograph are a bit distorted but if you select with care this can actually add to the effect.
I will post a copy of the filtered Babushka photograph so you can see what I mean.
I would love to construct the 4V form of a Icosahedron but I know that the maths is very difficult.
I feel that I can cope (the woodwork) with triangles with say approx 1.5 inch sides.
My first question is what would be the size of a 4V form ..... could I get it through my workshop door?
Errors in construction .... even a few minutes out in the 'Dihedrals' is a disaster... the sphere will not 'join' but if one sets the angles on the bandsaw with a good quality vernier protractor and makes all the component bits as accurate as possible then 'tightening the clamps' is really all that is neededto make minor adjustments.
Life gets a bit exciting when one gets to the last few pieces ..... then number of times that I have thought .... this is never going to join!
If anybody would like any assistance in constructing one of these models please contact me .... I find it is one of the most satisfactory projects that i have embarked on in years.
The selection of a suitable photograph is really the most important consideration. I could almost write a book on it.... one thing is that the left hand side of the print needs to look very similar to the right otherwise where they join will be very obvious. The photograph dose not have to exactly match... but if you had say part of a house at the left hand edge then it would look a mess.
If anybody is familar with Photoshop then it is possible to get a range of 'filters' that assist in sorting out photographs for different mathematical shapes .... If anybody is interested I will go into it further.