RHOMBIC ENNEACONTAEDRON

Geometrical study

   

 Here 2 sights of the same volume

It is well a zome, according to its definition: a polyhedron entirely composed of faces with sides parallel 2 to 2.

Its official name:the rhombic ennéacontaedron (only rhombuses).

 
 

  A zone being a band of facets broken around a parallel edge and which surround the volume, this one has 10 zones, 5 which touch the center and 5 external. On the figure, 2 zones are represented, and a face is born of their intersection.

 

I had some difficulties of representing me mentally this a little complex volume, or of drawing it. You not? I have to make a model of it to understand his simplicity and his beauty. Thus here what it contains.
   

 

 This volume is in fact made up only of 2 types of rhombuses, which one will call "Fat" and "Thin", of which here proportions.

 

 

Organization

5 fats gather out of star with 5 branches, 5 thin come around: veiled the top

5 figures similar viennet reffer around the top by sharing with him a thin rhombus

in consequence of the curve, the 2 losanes thin in red are not superimposed to do any more but one of them. Thus the 2 figures of bottom share a thin rhombus also

and so on for the 3 missing figures to put around the top

 

Here is a cross-section. A zome which resembles a dome. The thin rhombuses of bottom (out of orange) are vertical but they leave holes: one can transform them so that all the edges rest on the ground. And even to lengthen them downwards to have enough height for a door (so small volume). And finally to put caps of projection sufficient above these elements for protection the sun, the rain, and to channel the water of the roof in 5 points.

 Dimensions

For a length of common edge L = 1 (Recall: all the lengths are proportional to L and surfaces with the square of L)

Diameter on the ground There are in fact 2 parts: a long radius, center with the low point of the fatty rhombus = 2,8428 and one short rayof the center to between 2 of these points = 2,5716
that is to say a diameter of 5,4144

Height of the bottom of the fatty rhombus at top 2,8570

Height of the vertical parts (if not of extension) 0 - 0,7049 - 0,8925

Side on the ground = 1,6929

Surface on the ground = 21,485

Plane angles between fatty rhombuses = 15,5° between fat rhombus and thin rhombus = 22,2°

thus for a total diameter of 10 m, the length of the edges will be 1,865 m, the height of 5,256, the sides on the ground of 3,127 m, and surfaces it of 73,29 m2

To build

It will be necessary to carry out 30 FATTY rhombuses and 10 THIN rhombuses plus 10 vertical walls to lengthen by the bottom so necessary desired height

Conclusion

This zome offers a good volume with an important livable surface

The fatty losanes of the top have a weak slope (13°) and the thin ones a little more (32°). It will be necessary to look after the sealing on this level. The remainder has a strong slope (58 and 80°)

Like all the zomes integrating number 5, this one must generate good vibrations. The golden section is there of course present but hidden in the proportions.

To my knowledge, it was never carried out (like spaces livable)

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