One final unexplained button remains at the bottom of the GeoDome dialog: the Print button. This button is designed to print out a report of the input parameters you used to define the dome, and to give back to you some of the design parameters calculated for the dome, which may be of use to you during construction.
The report has three sections:
The first section returns in hardcopy your dome design parameters: the frequency, basis polygon, class, truncation factor, the dome wall thickness and the dome's radius. The truncated height (the height of the dome with the truncation removed) is also included. The base parameters include the number of straight segments making up the base, the base height, the base wall thickness and the base rotation value (as a percentage of the rotation from one segment to teh next). Derived values printed include the base radius, the wall segment length, and the total dome height, truncation and base included. Note that all these values are as displayed on the GeoDome dialog box.
The last section describes the face triangles. Remember that each basis solid face is developed into a series of smaller triangles. Each of these superfaces are identical, so describing the properties of one describes all the others. The "Symmetry Triangle" of the title is what Bucky called what I called a superface. The results in this section make no allowances for truncation of the whole sphere.
The symmetry triangle section starts by counting the things that make up this section of the sphere. The number of symmetry triangles is given, and the numbers of faces, edges and vertexes. You can get the total number of faces of the geodesic sphere by multiplying the number of faces per superface by the number of faces, but you cannot use the same technique to get the number of edges (struts) or vertexes, because they are shared with other superfaces.
The next section describes the struts (edges) that link the vertexes together. These are the most important figures to the builder, whether the dome is to be build with struts or with triangles. The superfaces are symmetric about their centers; that is, the face triangle lodged in each of the three corners of the superface are all the same; the three triangles which share an edge with those three are also identical, and so forth. Therefore all the measurements will show up in sets of three and six or higher multiples.
The vertexes are numbered outwards from one of the superface corners. 1 is always a superface corner; 2 and 3 join to 1, and so on. These vertex numbers are listed in the row marked "FromTo", each entry naming two vertexes. The row named Length gives the length of the edge that connects the two vertexes.
The symmetry triangle of a class 2 dome doesn't quite follow the underlying superface as it does with the class 1 dome. Instead, class 2 faces are divided up in a different way, because the faces merge across superface edges, and so the same way of counting does not hold. Instead, there are 60 symmetry triangles for an icosahedron, 40 for an octahedron and 12 for a tetrahedron basis. Each of these is identical, just as they are for the class 1 spheres. Since there are more of them, they are inevitably simpler than for class 1: each of the rectangles is divided by one half of the frequency; that is why class 2 domes only exist at even frequencies.
On the pictures here copied from a previous page The symmetry triangles can be seen. In the class 1 symmetry trinagle pretty wall tracks with the face of the solid. In the class 2 picture there are actually three symmetry trinagles shown, separated by the red lines - the third line of each triangle, which looks curved, is not really curved because it is projected along a geodesic of the sphere.
So there are more, simpler symmetry triangles in a class 2 than in a class 1 sphere.
GeoDome and the contents of this help file are
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