Listen To A Shape Polyhedral Apartment

Breaking Symmetry In Gold

RESIDENTS:Breaking symmetry in gold

“Chiral symmetry breaking yields the I-Au60 perfect golden shell of singular rigidity”

Mullins, et al., Nature Communication 9: 3352 (2018)

Nature sometimes behaves strangely by creating something odd from beautiful one. The authors of this paper witnessed such a phenomenon in gold, a precious metal. A golden shell made of 60 atoms in the shape of a rhombic icosidodecahedon having perfect symmetry (Ih-Au60) spontaneously transformed itself into a bizarre shape (I-Au60). The structure turned out to be a snub dodecahedron, one of the oddest Archimedean solids having a mirror-image counterpart. It was found that interatomic interactions between gold atoms (aurophilic interactions) were rearranged in such a way as to divide each square of the rhombic icosidodecahedron into two triangles. Accordingly, the coordination number (i.e. degrees of vertices) changed from 4 to 5, which increased atomic interactions. Moreover, the snub dodecahedron is known to be the most spherical Archimedean solid. As a result, the atomic cluster became compact and stable, creating a perfect golden sphere. This transition, however, depends on unique properties of gold atoms. The snub dodecahedral structure has been rare at a molecular level, and this golden sphere sheds light.
ROOM NO.:V60[560]F92[380512]

Snub dodecahedron

One of two Archimedean solids with chirality (the other one is a snub cube). It has 60 vertices (5-deg x60) and 92 faces (3-gon x80 and 5-gon x12). Icosahedral symmetry with chirality (I). Each vertex is uniform, surrounded by five faces of four triangles and a pentagon {3, 3, 3, 3, 5}. Making a space between pentagons of a dodecahedron followed by filling the gap with 80 triangles evenly results in a twist of pentagons either to the right or to the left. It is neat but mysterious. The isomorphic shape is obtained by dissecting each square into two triangles in the rhombic icosidodecahedron V60[460]F62[320430512] or by dissecting each hexagon into four triangles in the truncated icosahedron V60[360]F32[512620].

Rhombic icosidodecahedron

An Archimedean solid. It has 60 vertices (4-deg x60) and 62 faces (3-gon x20, 4-gon x30, and 5-gon x12). Icosahedral symmetry (Ih). Each vertex is uniform, surrounded by four faces of triangle, square, pentagon, and square {3, 4, 5, 4}. This shape is obtained by making a space between pentagons of a dodecahedron, and then filling the gap with squares at the position of the edges (30 in total) and triangles at the position of the vertices (20 in total) of the dodecahedron.

Polyhedral Apartment

Have you ever visit an apartment of polyhedra?


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