How to make a compound of five rhombihexecontahedra

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Ulrich
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How to make a compound of five rhombihexecontahedra

Post by Ulrich » Mon Jun 28, 2010 9:14 am

This is how a compound of 5 rhombihexecontahedra (RH) can be created:

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The RH is made of 60 rhombs with an acute angle of 63.4349 degrees. To build it, it is suitable to create a rhombihexahedron first. You can cut off a 3-sided pyramid with the angles you need fom the great rhombic triacontahedron (the dual of the great icosidodecahedron) with the facetting tool. You put this pyramid into memory 1 and augment one of the isosceles triangles by a prism. You facet this prism out and put it into memory 2. Then you retrieve the pyramid from memory 1 and augment all isosceles triangles by prisms. After that you augment all faces of the prisms looking towards the pyramid base face by the prism in the second memory and you have stella blend all coplanar faces. Now you have three rhombs of the wanted kind which you can facet out. Then you facet still four triangles and get a polyhedron like that:

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You augment the lateral triangles with prisms and afterwards the prisms' faces looking towards the bottom with the prisms from memory 2. Now you can facet out the rhombihexahedron.

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You put it into the memory 3 and augment it by itself in a suitable way until you have a rhombihexecontahedron.

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You put this into memory 4, choose the dodecahedron from the library, add the RH to it and put this into memory 5. You choose the compound of 5 dodecahedra from the library and excavate 5 suitable pentagons by the model in memory 5. All dodecadra will be eliminated, leaving behind a compound of 5 rhombic hexecontahedra.

Ulrich

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