Dome Truncations

In my opinion, using terms like 3/8 and 5/8 to refer to truncations of 3 frequency domes is nonsense. If one looks at a front view of a 3v geodesic,

it is apparent that there are nine rows of triangles, starting with the top pent.

This lends itself handily to truncations by ninths, not eights. It is not possible to divide an odd frequency dome into even truncations without modifying the bottom row of triangles. A 4/8 or 1/2 or hemispherical truncation is not practical.

If you remove the bottom four rows of triangles, you are left with a 5/9 truncation.

Leave off the yellow triangles to get a 5/9 truncation.

Notice that the bottom remaining row of tringles is (on average) vertical, so removing one more row of triangles

(remove the green triangles) will give you a 4/9 truncation which has the same floor area as a 5/9 truncation. The floors of these two truncations are rotated at 12 degrees relative to each other.

Remove another row of triangles

(remove the magenta triangles) and you now have a 3/9 truncation.

These are common truncations of 3v domes. The floor areas of the 4/9 and the 5/9 are the same, the floor area of a 3/9 truncation is smaller by about 22%, or you could say that the floor area of 4/9 or 5/9 is about 30% larger than a 3/9 truncation.

These numbers are based on a 12' radius dome.

Another consideration of truncations is the peak height.

These numbers are based on a 12' radius dome.

A 3/9 12'r 3v dome will have a peak height of 6.6' approximately, while a 4/9 will have a peak of 9.9', and a 5/9 will have a peak of 14.25'.