vZome’s Generate Polytope tool quickly generates the projections of several truncations of an Icositetrachoron. Each of these is centered on a predefined cell type. This post shows that for six of them, centering on another cell type produces one additional projection which can be build with Zometool. As soon as √2 scaling factors are needed, the corresponding vZome models are approximations.
Some projections can be modelled exactly in vZome's golden field, and can be build with Zometool blue, (half-)green and yellow struts only:
- rectified icositetrachoron centered on a cube
- rectified icositetrachoron centered on a cuboctahedron
- truncated icositetrachoron centered on a truncated octahedron
- truncated icositetrachoron centered on a cube
- cantellated icositetrachoron centered on a cuboctahedron
- runcinated icositetrachoron centered on a octahedron
An additional projection can be build exactly with Zometool, using blue, green, yellow and blue(-length)-green(-orbit) struts:
- cantitruncated icositetrachoron centered on a octahedron
The remaining projections require both blue-green and green(-length)-blue(-orbit) struts for an exact Zometool build:
- cantellated icositetrachoron centered on a octagonal prism
- bitruncated icositetrachoron centered on a truncated cube
- cantitruncated icositetrachoron centered on a rhombitruncated cuboctahedron
- runcitruncated icositetrachoron centered on a rhombicuboctahedron
- runcitruncated icositetrachoron centered on a truncated octahedron
- omnitruncated icositetrachoron centered on a rhombitruncated cuboctahedron
- disicositetrintercepted disicositetrachoron centered on a cuboctahedron
- disicositetrintercepted disicositetrachoron centered on a rhombicuboctahedron
The following vZome models show the building instructions for each of these projections. Additional scenes emphasize the cells of a specific type. Here, the number of cells is sometimes limited if it enhances the visual interpretation of the model.
