alphaZomes      for a human space
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Géométry 2

From Zonahedron to Zome
Zonahedron is a mathématical object

Zome is a built zonahedron
From one to other there is choises (matérials and building technics,...)

Axis position 
With vertical axis, it gives an esthetical volume, well balanced volume and with a great beauty.
But the axis van be tilted or horizontal
   
             

Zonahedra with vertical axis, tilted (2 positions) and horizontal

Cuts
For reasons of stability and habitability, zome is only a part of zonahedron
One can choise a plan to cut, may be equator for the even zomes, or behind equator for the odd zomes.
One can or not add walls to the
the even or odd zomes.
                          
Zome 6 without walls Zome 6 with walls
N * N/2 diamonds = 18
N triangles = 6
N * (N/2 - 1) ldiamonds = 12
N triangles+walls = 6

Zome 5 without walls Zome 5 cwith walls
N * (N - 1) /2 diamonds = 10
N triangles = 5
N * (N - 1) /2 diamonds = 10
N murs trapèzes) = 10
             

Dimensions
Next table gives for various N the maximal dimensions obtained with a given size of sides (2 m) and two classical form numbers.

For the odd zomes 5 and7, it are ground dimensions for a zome without walls

N Côté Diamètre Surface
4 3,40 - 3,58 4,80 - 5,05 11,60 - 12,80
5 3,20 - 3,40 5,00 - 5,20 18,00 - 19,90
6 3,40 - 3,58 6,80 - 7,15 30,00 - 33,25
7 3,30 - 3,50 7,25 - 8,00 40,00 - 44,20
8 3,40 - 3,58 8,90 - 9,35 55,90 - 61,80
10 3,40 - 3,58 11,00 - 11,55 89,00 - 98,5
12 3,40 - 3,58 13,15 - 13,80 129,50 - 143

Extensions

We can add volumes to create more space
   

        Extension with a 1 slope or 2


Extension with a part of zome or a whole zome
Zones
We call zone a bande of facets which surrounds the volume. One of the sides of facets remains parallel to a direction. These zomes wraps around the zome in spirals. A facet is created by the intersection of two zones.


In "classical" zomes , there are so many zones as lthe N number. However one can add or to stake axay one or several zones from a zonahedron, or to distort them: they will acquire another zome.
Two types of often met zones: (for instance on this zome 6)



M zone: plan is cut in a median, both separated halves, and a zone was introduced between both parts


D zone: plan is cut in a diagonal, both separated halves, and a zone introduced between both parts


By introducing one or other of these zones allows an enlargement of the surface of the zome without augmenting either complicacy or height of the volume. Hexagons are created at intersection of three zones.