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Space Frames and Geodesic Domes 10/16/07

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Five Platonic Solids An important group of three dimensional shapes are the five platonic solids. These include: tetrahedron (4), Cube (6), octahedron (8), dodecahedron (12) and icosahedron (20). These are the only shapes whose faces are all identical regular polygons.

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**Space Frame A truss system with members that lie in three dimensions.**

Two usual forms tetra-hedron (three-sided pyramid) half-octahedron, i.e. (four-sided pyramid)

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Tetrahedron The tetrahedron is all triangles and clearly more stable.

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Octahedron Half-octahedron’s square side makes it more convenient for most construction projects. Rigid joints are required to prevent the angles from changing.

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**Redundancy A space frame system consists of layers of struts**

Some struts are connected to the supports (columns), Others radiate outwards from those. Any applied loads have many choices of route to get to supports at corners; This provides a redundancy in case one member is broken and makes space frames safer.

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Are Members Identical? Are all the members of the space frame identical? The structure usually repeats The elements closest to the supports take the most weight. The elements closest to the supports are thicker than those farther away.

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**Famous Space Frame Entrance to Louvre**

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Biosphere 2 in Arizona

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**Connectors Very important pieces for any space frame**

the connections between the members. Two common types of connector Unistrut Mero, with spherical connectors

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**Spherical Shapes Geodesic Dome are spherical space frames.**

The most standard method uses a three-frequency subdivision of an icosahedron, a soccer ball, a system surrounded by hexagons. Developed and patented by Buckminster Fuller ( )

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Buckminster Fuller

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Characteristics Geodesic domes enclose a great deal of space without interior supports; thus they are efficient structures for heating and cooling. A difficulty with them is that it can be hard to remove struts to make convenient openings for doors or windows. Many people like the shape, and build houses from them.

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**Support through compression and tension**

Geodesic domes have most members in compression However, the lower horizontal struts can be in tension.

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Large domes Just as with cables, the less horizontal a given strut is, the less compression it needs to withstand an applied load. Having very few joints leads to a stronger structure, less smooth – space is used inefficiently. A way around this issue is to have two concentric domes, and run the struts from one to the other, allowing the truss depth to be larger. This method is generally necessary to have larger geodesic domes.

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Montreal’s Biosphere

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Epcot Center

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VIDEO! Video about geodesic domes and Buckminster Fuller ( )

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3-D Geometry By: _____. Platonic Solids These platonic solids were made with Zometools. A platonic solid is _____ There are five platonic solids.

3-D Geometry By: _____. Platonic Solids These platonic solids were made with Zometools. A platonic solid is _____ There are five platonic solids.

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