The connection between circle packings and geodesic domes is well known. Here we would like to introduce some geodesic hyperdomes (which are dense packings on the 3-sphere S3) which are derived as decorations of regular polytopes. The initial purpose was to generate theoretical models for amorphous metals by mapping these structures from S3 to the Euclidean space R3. These structures have also been used in the field of icosahedral quasicrystals and also to describe finite clusters with non-crystalline symmetry.
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