
Geometry
(continued)
From Zonaedron to Zome
The zonaèdre is a mathematical, unreal being
The zome is a constructed zonaedreon
From one to the other, choices are made (materials and construction
techniques, habitability, etc.)
Axis position
Generally, the axis of the zome is positioned
vertical, but it is not an obligation
Vertical, it leads to aesthetic, wellbalanced volumes and great
rigidity
But we can also position this oblique axis, or even horizontal
Zonaedron
6 with vertical axis, inclined (2 positions) and horizontal (2
positions)
Cups
For
reasons of stability and habitability, the zome is only a portion of
zonaedron
We must therefore choose a section plane, either the equator plane for
even order zomes, or the plane below the equator for odd numbers.
In these 2 cases, we may or may not extend the zome by vertical walls
In even zomes, the crown at the equator is vertical (parallel to the
axis), this is not the case for odd numbers

Zome 6 cut under
the equator and resting on triangles 
Zome 6 cut at
the equator and extended by walls 
N *
N/2 diamonds = 18
N triangles = 6

N * (N/2  1) ldiamonds = 12
N
triangles+walls = 6 



Zome 5 cut under
the equator and resting on triangles 
Zome 5 cut above
the equator and extended by walls 
N * (N
 1) /2 ldiamonds = 10
N
triangles = 5

N * (N
 1) /2 diamonds = 10
2 *
N walls
= 10

Dimensions
For a given edge length, the higher the order number, the larger the
zome
The following table gives for various N the (approximate) dimensions
obtained with an edge length of 2 m and two of the most common shape
numbers. These are maximum dimensions not to be exceeded. Reduce the
edge to stay below.
For odd zomes 5 and 7, these are the dimensions on the ground for a
zome without walls (reentering)
N 
Side 
Diameter 
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
These are volumes that are added to
enlarge the living space (or create separate rooms)
This is easy with evenorder zomes with vertical walls
Extension
with roof with 1 slope and roof with 2 slopes
Extension by part of zome
and by grouping with another zome
Zones
A continuous band of facets which
surrounds the volume is called the zone. One of the edges of the facets
remains parallel to a direction. These zomes are the seat of spiral
zones. A facet is created by the intersection of two zones.
In "classic" zomes, there are as
many zones as the zome order. However, one can add or suppress one or
more zones of a zonaèdre, or else deform them: we will still obtain a
zome.
Two types of frequently encountered zones: (for example on this zome 6)
Zone M: the plane is cut
along a median, the two halves separated, and a zone is introduced
between the two parts
Zone D: the plane is cut along a diagonal,
the two halves separated, and one is zone introduced between the two
parts
The introduction of one or other of these zones makes it possible to
enlarge the surface of the zome without increasing either the
complexity or the height of the volume. Hexagons are created at the
intersection of 3 zones.
