Math Is Fun Forum

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?

Soapy Joe

My first attempt to input your angles into a sketch of the Icosahedron  has, I am afraid, rather landed onto rocky ground.

I feel O.K. about sides CDEF but a bit confused about A and B

Not quite sure if this scan is any use....

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.

Soapy

Yes, This triangle is an equilateral designated the letters FFF.

I will most probably be building my sub-assemblies around this particular triangle.

Soapy

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.

Soapy

This really is the only drawing that I needed for the 3V

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'.

Soapy

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.

Great fun!

Soapy

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.

Soapy

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.

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.

soapy.

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.