There are one hundred and twenty vertices which all belong to the hypersphere S with radius equal to the golden ratio (φ = ⁠ 1 + √ 5 / 2 ⁠) if the edges are of unit length. The six hundred cells are regular tetrahedra grouped by five around a common edge and by twenty around a common vertex. This structure is called a polytope (see Coxeter) which is the general name in higher dimension in the series containing polygons and polyhedra. Even if this structure is embedded in four dimensions, it has been considered as a three dimensional (curved) manifold. This point is conceptually important for the following reason. The ideal models that have been introduced in the curved Space are three dimensional curved templates. They look locally as three dimensional Euclidean models. So, the {3,3,5} polytope, which is a tiling by tetrahedra, provides a very dense atomic structure if atoms are located on its vertices. It is therefore naturally used as a template for amorphous metals, but one should not forget that it is at the price of successive idealizations.