This page gives step by step instructions showing how to construct a geodesic dome with a geometry similar to the Saint Louis Refrigerator Car Dome at Wood River, U.S.A. The subdivision frequency and truncation plane are different in this example.
Photograph © Karl Hartig. (Used with kind permission of the photographer).
This demonstration is split into two parts; Part 1: Manifold and Spaceframe; and Part 2: Hubs and Struts.
Part 1: Manifold and Spaceframe
1. Switch to ‘Target A’ and create a new 5V icosahedral subdivision using Class I and Breakdown Method 1.
2. Select the Pick Element tool with the Pick Vertex tool on the Toolbar. It is desired to truncate the sphere using the Theta value of the vertex in the yellow circle. Click on this vertex; the Theta value given in the Vertex Editor is:
When the area selection is made, the Vertex Editor fields initialize to zero:
83.82058954in the Theta field and press return. All the selected vertices are given the new Theta.
4. Bring up the Truncate/Range Adjust window by clicking the button on the Toolbar. Enter
83.82058954 for ‘New’, 83 for Min, and 84 for Max. All vertices with Theta values between ‘Min’ and ‘Max’ will be assigned the ‘New’ value.
5. The ‘spaceframe’ for this dome will be the Primal manifold of ‘Target B’. Switch to ‘Target B’. Here the manifold of ‘Target B’ is shown in yellow.
6. Create an identical 5V icosahedral subdivision using Class I and Breakdown Method 1. Then Perform the same Area Select and truncation as for ‘Target A’.
7. Swicth back to ‘Target A’. Select menu ‘Modify’->‘Generate Dual’:
8. Bring up the Envelopes window by clicking the button on the Toolbar. Click the ‘Dual’ tab of the Envelopes window and set the Dual Offset of ‘Target A’ to
9. Select menu menu ‘Modify’->‘Make Trifans...’. Select options ’Dual’ manifold, ‘Visible cells’ and ‘Group Sectors by Operation Count’. Click Apply.
Trifans are created in the Dual manifold and the Primal updates to reflect the new Dual geometry. Note that because the Dual cells were trifanned, the Primal manifold now resembles the old Dual before trifanning occured. Do not worry that the Primal floor no longer lies on the truncation plane. The Primal manifold of ‘Target A’ is no longer required, so hide the Primal geometry using the Attributes window. This leaves the trifanned Dual cells of ‘Target A’ and the Primal manifold of ‘Target B’:
10. Whilst still on ‘Target A’, make the Dual cells visible by clicking the Dual cells button on the ‘Dual’ tab of the Attributes window:
11. Select menu ‘Modify’->‘Project Target A Dual Trifan centroids to corresponding Target B Primal vertices’.
The Dual centroid of Target A are projected. This completes Part 1: Manifold and Spaceframe.
Part 2: Hubs and Struts
1. Switch to ‘Target B’. Before contructing the hubs and struts, there is the small matter of adjusting the Primal envelope extents of ‘Target B’ to account for the hub depth. It so happens that in this particular example, the Units (set in the Preferences) are in Feet and Inches. Hence the Actual Extents in the Envelope window are given in decimal feet. A hub dimension with a depth of
1 inch has been chosen; this gives
0.5 inches above and below the hub plane. To ensure that the bottom of hubs do not intersect with the Dual stellations of ‘Target A’, the Primal envelope extents of ‘Target B’ must be increased by half and inch. There are
12 inches to a foot, so the decimal foot value for
1 inch is
10/12 = 0.8333333r. Half this value is
0.41666666r. The extents in the Envelope window are set as:
2. Choose ‘Generate Hubs’ from the ‘Hubs’ menu. Bring up the ‘Struts and Hubs’ window by choosing menu ‘Hubs’->‘Set properties...’. Click on the ‘Primal Hubs’ tab and enter the following parameters:
3. To construct the Primal struts for ‘Target B’, choose ‘Generate Struts’ from the ‘Struts’ menu. Bring up the ‘Struts and Hubs’ window by choosing menu ‘Struts’->‘Set properties...’. Click on the ‘Primal Struts’ tab and enter the following parameters:
Note that ‘Elongate Hub Intersection Cylinder’ is checked because the hub depth is less the the strut depth.
The completed dome should look similiar to the following screenshot: