On the self-similarities of two icosahedral patterns
Abstract
The vertex set Q of the usual three-dimensional Penrose tiling whose strip projection construction starts from an icosahedron is invariant under an infinity of affine similarities r ↦ τ3(r − q) + q having as centers certain points q ∈ Q and the scaling factor τ3, where τ = (1 + [unk])/2. A similar construction done by starting from a dodecahedron leads us to an icosahedral pattern Q′ invariant under the similarities r ↦ (5 + 2 [unk]) r and r ↦ (4 + 2 [unk]) r. These new self-similarities whose determination is based on the decomposition into irreducible components of a representation of the icosahedral group can not be obtained by using the method recently reported by Masáková, Patera, Pelantová (J. Phys. A: Math. Gen. 31 (1998) 1443).
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Articles in the same Issue
- On the self-similarities of two icosahedral patterns
- Conformation of single chains of anion-centred edge-sharing tetrahedra
- X-ray and neutron reflectivity
- Anisotropy of Anomalous Scattering: a tool for phase information
- Structure and temperature transformation of SnSe. Stabilization of a new cubic phase Sn4Bi2Se7
- The new heteronuclear cluster cation [GeGa4]8+ in GeGa4S4: a summary of single crystal and mixed crystal studies
- Dimorphic YbPdSn with ZrNiAl and TiNiSi type structure
- The structure of the ternary phase Co2NiAl9 (Y2)
Articles in the same Issue
- On the self-similarities of two icosahedral patterns
- Conformation of single chains of anion-centred edge-sharing tetrahedra
- X-ray and neutron reflectivity
- Anisotropy of Anomalous Scattering: a tool for phase information
- Structure and temperature transformation of SnSe. Stabilization of a new cubic phase Sn4Bi2Se7
- The new heteronuclear cluster cation [GeGa4]8+ in GeGa4S4: a summary of single crystal and mixed crystal studies
- Dimorphic YbPdSn with ZrNiAl and TiNiSi type structure
- The structure of the ternary phase Co2NiAl9 (Y2)
