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Dome Radius:3.00
Stru
tLength
Dom
e
Spher
e
A 0.759
30 60
B0.885
30 60C 0.883
60 120
D 0.938
70 120
E 0.974
30 60
F 0.895
30 60
4-way
connectors20 0
5-way
connectors 6 12
6-way
connectors65 150
The Theory
Platonic And
Archimedian
Solids
Face Variations
Projection
Variations
Truncations
Variations
Why Choose
Geodesic?
A geodesic is a line joining two points on the surface of the earth. A geodesic
structure is one that follows the surface geometry of a sphere. But there are many kinds
of dome structures that do this. What defines a dome as a geodesic structure? Geodesics
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Unlimited follows the lead of the Surrey University Space Structures Research Centre,
which, in our view, is the worlds leading authority on the configuration of space frame
structures, of which the geodesic dome is one. So here below are the main varieties of
domes, their names, and their defining features.
Schwedler Dome
This has ribs extending down from the crown
of the dome, rings extending horizontally
around the dome, and diagonals extending
from intersections between ribs and rings on
one horizontal ring to those on the next .
Ribbed Dome
This has ribs extending down from the crown
of the dome and rings extending horizontally
around the dome.
Lamella Dome
This has diagonals extending from the crown
down towards the equator of the dome, in
both clockwise and anti-clockwise directions,
and may or may not have horizontal rings,
but has no meridional ribs.
Diamatic Dome
This has what may be described as pie-
shaped sectors repeated radially around the
crown. Here, the apex of each sector has a
width of zero and, at its base, a sector is 360
degrees divided by the number of sectors .
Great Circle Dome
This is a dome not defined by the Space
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Structures Research Centre. We call it the
Great Circle Dome as all of its elements
follow more or less great circular paths over
the surface of the dome.
Geodesic Dome
This dome is rather different in its origins. It
is derived from one of the platonic or
Archimedean solids, or from a prism or anti-
prism - seePlatonic and Archimedean Solids,
and below.
Take for example the Icosahedron, which is a
platonic solid with 20 regular triangular
faces.
We take any face of this solid and subdivide
it in any way we choose, for example as in
the drawing on the left.
We then take this pattern, and project each
intersection in the pattern outwards onto the
surface of the sphere on which all the vertices
of the original icosahedron sit.
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We then replicate this around the whole of
the icosahedron, as left. We also have the
options of using a different base solid, a
different projection, a different face pattern,
and a different portion of the sphere. Thesepossibilities are explored in the following
pages
Platonic And Archimedian Solids
The Platonic and Archimedian solids (see the pictures below) are polyhedra, 3D shapes,
that are either completely regular in all respects, as are the platonic, or semi-regular, as
are the archimedian.
The platonic solids have regular length edges, are regular in size and shape of faces, and
have regular angles throughout. There are five of these.
The archimedian solids are variants of the platonic solids and have regular length edges,
but have two or three different faces. The angles are regular within a face, but vary from
face to face.
The choice between polyhedra as a starting point for a design depends upon the function
and desired aesthetics of the final structure. For example, a dome that wants to sit as a
conservatory in a corner between two wings of an existing building would be best as aquarter of a polyhedron with fourfold symmetry, such as the octahedron, but a free
standing greenhouse could be based purely on desired aesthetics and any of the
polyhedra could be used as a starting point.
The drawing below shows the five platonic polyhedra and how the archimedian
polyhedra are derived from them.
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Face Variations
Whichever polyhedron is the basis of our geodesic, we must decide upon a pattern to
map on to those of its faces we are going to use in our final structure. We may map any
pattern at all onto a face, and choose as many different patterns as there are faces, or
indeed map more than one pattern on to a face, or create layers of patterns on to faces to
create double or treble layer grid domes. Here we will use the icosahedron as the base
polyhedron and have a look at just a few possible face patterns we could choose.
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2 Frequency Triangulation
This is the simplest version, where we simply divide each edge of the triangle in two
and join each created mid-point to the next.
3 Frequency Triangulation
This is exactly as above except that we divide each edge into three.
6 Frequency Triangulation
Again a simple pattern, this time dividing each edge into six.
Projected 6 Frequency Pattern
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Here the pattern from the image immediately above has been projected to create the
geodesic triangle from the now patterned icosahedral one.
Geodesic projection of another single layer face pattern
This time a greater variation in final triangle size results from a variation in triangle sizein the pattern mapped on to the original icosahedral triangle.
Geodesic projection of a star onto a dodecahedral pentagon
This time a pentagon has been used since a star does not fit on to a triangular face. The
dodecahedron is a suitable base polyhedron for this.
Geodesic projection of another pattern mapped on to an icosahedral face.
Another more complex pattern is used here. The resulting dome is dimpled.
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A double layer of hexagons
Here we have a double layer grid that sits within a triangle.
Geodesic projection of above hexagonal double layer grid
The double layer grid now curves around the surface of our sphere.
Geodesic projection of above double layer grid created from the top five triangles of an
icosahedron
Projection Variations
Following our choice of base polyhedron, in this case the icosahedron, the portion of it,
in this case the upper half, and the face pattern, in this case a pattern of 16 triangles to
each face, we then have a variety of projection variations to choose from. Projectionrefers to the way in which our choice of now-patterned polyhedron is projected on to a
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surface, and also to the choice of surface. Here we shall be using projection outwards in
all directions away from a chosen point, but we will be looking at projection on to a
variety of different surfaces.
Projection on to a Sphere from the centre of the Icosahedron
Here our half icosahedron becomes a hemisphere and all our triangles are projected
evenly. The point of projection is the centre of the original icosahedron.
Projection on to a Sphere from above the centre of the Icosahedron
Here our half-icosahedron becomes more than a hemisphere, and the triangles are
projected unevenly, because the point of projection is now closer to the top of the
original icosahedron
Projection on to a Sphere from above the centre of the Icosahedron, and to one side
Here our dome again becomes more than a hemisphere and the triangles are all biased
towards the point of projection.
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Projection on to an Ellipsoid
Here the original sphere onto which the Icosahedron has been projected has beenelongated both horizontally and vertically. The projection is central.
Projection on to an Ellipsoid
This is another version of a central projection on to an ellipsoid
Projection onto a Paraboloid
This time the surface onto which we are projecting is a paraboloid.
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Projection onto an Elliptical Paraboloid
Now our surface is an elliptical paraboloid. This is again a central projection.
Projection onto a Hyperboic Paraboloid
Now our surface is a hyperbolic paraboloid.
Projection onto a Cone
Here our surface is a cone.
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Projection onto an Elliptical Cone
Now our surface is a cone that is stretched both vertically and horizontally.
Truncations Variations
Following our choice of base polyhedron, in this case the icosahedron, the portion of it,
in this case the upper half, and the face pattern, in this case a pattern of 16 triangles toeach face, we then have a variety of projection variations to choose from. Projection
refers to the way in which our choice of now-patterned polyhedron is projected on to a
surface, and also to the choice of surface. Here we shall be using projection outwards in
all directions away from a chosen point, but we will be looking at projection on to a
variety of different surfaces.
Full Sphere
Three Twelfths
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One Third
Five Twelfths
Hemisphere
Seven Twelfths
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Two Thirds
Nine Twelfths
Ten Twelfths
Why Choose Geodesic?
The Advantages of Using a Geodesic Design
1. Geodesics offer the strongest form of architecture known (because geodesic forms
follow a doubly curved surface and because the base is always a polyhedron which
already begins to approximate a sphere. The example of the strength of the shell of an
egg confirms the strength of a spherically based structure).
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2. A geodesic form creates the largest volume of space covered by the least amount of
material (the most efficient use of material to cover a given volume of space).
3. The largest unobstructed spans can be created using geodesic geometry.
4. Geodesic structures provide the most efficient form for the purposes of heating.
5. Spheres are aesthetically highly pleasing.
6. Spheres generate and embody potent energy fields.