Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples

Ramsden, S.J.; Robins, V.; Hyde, S.T.

doi:10.1107/S0108767308040592

Acta Crystallographica Section A
Acta Crystallographica
Section A FOUNDATIONS AND ADVANCES

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Figure 16
Left: two U-tilings with $[\star{\tt 2224}]$ symmetry obtained via a split from a $[\star{\tt 2}]$ – $[\star{\tt 2}]$ edge to the opposite $[\star{\tt 2}]$ – $[\star{\tt 4}]$ edge, followed by a glue across the other $[\star{\tt 2}]$ – $[\star{\tt 4}]$ edge, derived from QC2566. These tilings are distinct embeddings of a single D symbol and therefore generate different surface reticulations. To illustrate this, we show the projections onto the P surface (centre) and resulting s-nets (right). Tiling and net labels are described in §§5.1

and 6.3

FOUNDATIONS
ADVANCES

ISSN: 2053-2733

Volume 65| Part 2| January 2009| Pages 81-108

doi:10.1107/S0108767308040592

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