## Eden Project Dome Demonstration

This page gives step by step instructions showing how to construct a geodesic dome with a spaceframe geometry similar to the Eden Project domes in Cornwall, U.K. This page contains 33 screenshots and is graphics intensive.

Above: the overall geometry. The inner Dual manifold of ‘Target A’ has been smoothed. In summary, the edges are divided in two; the divided edges are then joined up to make new faces. Finally, the original Dual vertices are truncated to create triangular EPD faces (EPD is my acronym for ‘Eden Project Dome’). Finally, the Dual vertices in ‘Target B’ are connected to the EPD faces in ‘Target A’, thus forming a spaceframe of pyramidal struts. In this demonstration, the distance between inner and outer manifolds has been increased exorbitantly to make things clear.

Above: detail of the geometry. For each vertex in the Dual manifold of ‘Target B’, spaceframe members are created that connect to the corresponding Dual EPD faces of ‘Target A’.

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 6V icosahedral subdivision using Class I and Breakdown Method 1. Switch to the front camera by right-clicking in the OpenGL view and choosing ‘Front’ from the pop-up menu. In this instance, a range truncate will be performed in the red horizontal band...

2. Select the Pick Element tool with the Pick Vertex tool on the Toolbar. We want the vertex with the highest Theta value in the horizontal band. This is vertex A in the yellow ring. Click on this vertex and note the Theta value in the Vertex Editor on the Toolbar.

3. The Theta value is given as `100.81231696`. Copy this Theta value to the clipboard.

4. We now want the vertex with the lowest Theta value in the horizontal band. This is vertex B in the yellow ring. Once again click on this vertex and note the Theta value in the Vertex Editor. The value is given as `99.88314549`.

5. The Theta value is given as `99.88314549`.

6. Bring up the Truncate/Range Adjust window by clicking the button on the Toolbar. Paste the hightest Theta value into the ‘New’ field from the clipboard. Whilst noting the lowest Theta value (which is still displayed in the Vertex Editor), choose appropriate values for ‘Min’ and ‘Max’. All vertices with Theta values between ‘Min’ and ‘Max’ will be assigned the ‘New’ value.

Ensure that ‘Project to Envelope’, ‘Truncate after adjustment’ and the ‘Make dual sit flat’ options are checked, then click Apply. Click Done to close the window. The sphere is truncated at Theta value `100.81231696`.

7. Select menu ‘Modify’->‘Generate Dual’, then switch back to the orbiter camera by right-clicking in the OpenGL view.

8. Smooth the Dual by selecting menu ‘Modify’->‘Split Edges | Make Faces | Truncate Corners...’ Then select the Dual manifold option.

The dual is smoothed:

9. 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 smoothed Dual cells:

10. Switch to ‘Target B’. Here the manifold for Target B is shown in yellow.

11. Create an identical 6V icosahedral subdivision using Class I and Breakdown Method 1.

12. Truncate ‘Target B’ using the same parameters as for ‘Target A’.

13. Whilst still on ‘Target B’, bring up the Envelopes window by clicking the button on the Toolbar. Set the Primal XYZ extents to 1.1.

14. Whilst stiil on ‘Target B’, Select menu ‘Modify’->‘Generate Dual’:

15. The Primal manifold of Target B is no longer required so hide it using the Attributes window:

16. Create the spaceframe by selecting menu ‘Spaceframe->Target B Dual Vertex to Target A Dual EPD Face’. This completes the construction of the manifolds. It is now time to create the hubs and struts...

### Part 2: Hubs and Struts

In the following screenshots, the ability to hide targets was used in the ‘View’ menu so as to make things clear.

1. To construct the Dual hubs for ‘Target A’, switch to ‘Target A’ and choose ‘Generate Hubs’ from the ‘Hubs’ menu. Bring up the ‘Struts and Hubs’ window by choosing menu ‘Hubs’->‘Set properties...’. Click on the ‘Dual Hubs’ tab and enter the following parameters:

2. To construct the Dual struts for ‘Target A’, choose ‘Generate Struts’ from the ‘Struts’ menu. Bring up the ‘Struts and Hubs’ window by choosing menu ‘Struts’->‘Set properties...’. Click on the ‘Dual Struts’ tab and enter the following parameters:

3. Click ‘Apply Hubs’ and ‘Apply Struts’. Colour the Dual hubs and struts for ‘Target A’ using the Attributes window. Below is the completed manifold for ‘Target A’:

4. To construct the Dual hubs for ‘Target B’, switch to ‘Target B’ and choose ‘Generate Hubs’ from the ‘Hubs’ menu. Bring up the ‘Struts and Hubs’ window by choosing menu ‘Hubs’->‘Set properties...’. Click on the ‘Dual Hubs’ tab and enter the following parameters:

5. To construct the Dual 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 ‘Dual Struts’ tab and enter the following parameters:

6. Click ‘Apply Hubs’ and ‘Apply Struts’. Colour the Dual hubs and struts for ‘Target B’ using the Attributes window. Below is the completed manifold for ‘Target B’:

7. To construct the Spaceframe struts, choose ‘Generate Spaceframe Struts’ from the ‘Struts’ menu. Bring up the ‘Struts and Hubs’ window by choosing menu ‘Struts’->‘Set properties...’. Click on the ‘Spaceframe Struts’ tab and enter the following parameters:

8. Click Apply Struts. Colour the Spaceframe struts using the Attributes window by selcting the correct node of the Spaceframe tab (it should be coloured red). Below is the completed spaceframe:

9. The final design should look similar to the screenshot below:

10. Showing the Dual cells for the inner manifold of ‘Target A’ makes the spaceframe geometry a little clearer:

11. The outer manifold for ‘Target B’: