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Keywords
We investigate a 3-dimensional analogue of the Penrose tiling, a class of 3-dimensional aperiodic tilings whose edge vectors are the vertex vectors of a regular icosahedron. It arises by an equivariant projection of the unit lattice in euclidean 6-space with its natural representation of the icosahedral group, given by its action on the 6 icosahedral diagonals (with orientation). The tiling has a canonical subdivision by a similar tiling ("deflation"). We give an essentially local construction of the subdivision, independent of the actual place inside the tiling. In particular we show that the subdivision of the edges, faces and tiles (with some restriction) is unique.
Geometrie und Kosmologie
(1990)
We show that every isometry of an extrinsic symmetric space extends to an isometry of its ambient euclidean space. As a consequence, any isometry of a real form of a hermitian symmetric space extends to a holomorphic isometry of the ambient hermitian symmetric space. Moreover, every fixed point component of an isometry of a symmetric R-space is a symmetric R-space itself.
Muster, Fliesen, Symmetrie
(2001)
