Geodesic
An Essentially-three-dimensional Quasicrystal
As the generator of an essentially-3-D quasicrystal, some detail of a 3-D Penrose transformation is given. The expansion rate t3=4.236 is by far the larger than ever believed value t=1.618. The features of this model agree rather well with those of high-resolution electron micrograph. The Penrose logic of hierarchic generation of patterns is summarized and a new expression is also given for 2-D Penrose transformation.
Classification : 52C23 
@article{VM_1999_1_4_a3,
     author = {Tohru Ogawa},
     title = {An {Essentially-three-dimensional} {Quasicrystal}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_1999_1_4_a3/}
}
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Tohru Ogawa. An Essentially-three-dimensional Quasicrystal. Visual Mathematics, Tome 1 (1999) no. 4. http://geodesic.mathdoc.fr/item/VM_1999_1_4_a3/