Strange rhombic pyramids

[rolly_wood]

hi all.
I had an idea seeing the dodek puzzle: why not a multi-colours "les pleiades" (P. Dubois). The hexahedra at the vertexes can be decomposed into 3 rhombic pyramids (RP)as in Figure. Each of which may be chosen with a different wood so having a puzzle of 6 or 12 different woods. The difficulty would be related not only to assemble the right interweaving of 4-hedra but to choose the right wood.
The problem seemed to me being related to this RP that it is not equal to that of RD based puzzle. This latter has angles of 70.5 109.5 the rhombus, 70.5, 54.7, 54.7 the sides, instead that needed for les pleiades should have 72 108, the rhombus, 72,54,54 the sides, slightly different indeed.
I calculated if it could be possible to obtain that with the Coffin procedure based on triangular sticks, and rather surprisingly the answer is YES.
For RD-based puzzles miter should be set to 35.26, for platonic 12hedral puzzle to 36 but the procedure remains valid..
 

EDIT sorry the wrong order of the last pictures

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[Canuck]

Very interesting Rolly  

[Chinnomotto]

Rolly, Rolly, Rolly,

It took me 5 gos, reading your post and seeing the pics before I got what you are getting at.

So lets see this little project in 3 woods, it will be absolutely stunning

So differcult to cut the pieces accurately

You just forund the link between a regular dodecahedron and the rhombic dosecahedron

Well done mate, least your cortex is working fine, Cheers

[rolly_wood]

Rolly, Rolly, Rolly,
It took me 5 gos, reading your post and seeing the pics before I got what you are getting at.

of course is due to my limits in explaining what I meant, writing in a non native language about 3d angle and strange shapes, is not so easy

So differcult to cut the pieces accurately

Yes but "les pleiades" is robust against inaccuracies, provided the angles are right the hexahedra may be sanded even removing half mm without problems

You just forund the link between a regular dodecahedron and the rhombic dosecahedron

right:
http://mathworld.wolfram.com/Dodecahedron.html
http://mathworld.wolfram.com/RhombicDodecahedron.html
EDIT oh: you mean found! I did not find it, there is not: roughly speaking RD is based on sqr(2), dodecahedron on srq(5)  

thank you Stephen (and John), I need to maintain neurons trained 


EDIT what about your method for RP (RD based)? square or triangular stick?

[Johan Heyns]

Rolly

I've had this translated by a language expert in Afrikaans, and he told me that I was completely nuts in trying to make him translate gobbledygook.

I'll just observe from a long distance and leave this to the MENSA IQ level people like Rolly and that dentist down under that Duck Poo Chair. 

From the little that I understand, it sounds as if you know what you are talking about.  Well Done!!!   

Please translate to African English so that I can understand or at least make an attempt at understanding!!

[rolly_wood]

From the little that I understand, it sounds as if you know what you are talking about. 

  not sure of it.
Coffin mentions a method to obtain rhombic pyramids (which is a dissection product of rhombic dodecahedron) from triangular sticks. It is that of the figure, cut a 35.25 degrees rotate 120 degrees the stick and advance it, cut again and so on to obtain such pyramids without waste.
For doing a variation of "les pleiades" with 6 or 12 woods, it needs similar pyramids but looked in details they show to be slightly different.
Well I think, I have not tried yet, that anyway the Coffin method is still valid provided to set the mitre to 36 instead of 35.25. Stephen says that I have found the link between rhombic and regular 12hedra, but he jokes.... there is no link I believe they are polyhedra of different "families". Someone simplifying the matter says the RD is based on the square root of 2, 12hedron instead is based on phi and, consequently on the square root of 5
Hope to have not augmented the confusion  at least

[rolly_wood]

Johan, does your silence mean that my explanation was not understandable at all?     Are you upside down there? Perhaps you need to flip the figures.. .   

[Johan Heyns]

Hi Rolly

No,  My silence is attributable to a more basic need.  I had a braai (barbeque) in the time that passed.  A proper 750 gram rump steak to perfection. 

I'm still stumped with your stuff though.  Even that nice Chardonay I had with the steak did not help my unnerstanding at all.  I fact, I think I'll have a good nights rest before I attempt to tackle the complexities of dodecahedrons and mad metagrobologists again.

[Canuck]

  I had a braai (barbeque) in the time that passed.  A proper 750 gram rump steak to perfection. 

And I thought you were a vegetarian!

[rolly_wood]

  Chardonnay (white, at least here it is so) with steak?  You are strange in the other hemisphere : RED is mandatory with grilled meat....
 

[Johan Heyns]

Rolly,  red wine gives me a headache.  Remember, the steak is dripping with blood, so that enough red.
I just wave the meat at the flames then I eat it.

[rolly_wood]

, the steak is dripping with blood, so that enough red.

[LEAP]

You guys are making me hungry!

I'm with you Johan, singe the edges and drop it on the plate. Steak looses all the flavor when it turns all brown.

[rolly_wood]

IMHO fish is better, are we not talking about rhombus? 

[rolly_wood]

... and rather surprisingly the answer is YES.

I said it was surprising! ... something did not convince me I redid the calculation and found a mistake. Probably the answer is as expected: NO
 
I will post confirmation soon