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 5
The dodecagonal region of the hyperbolic plane that forms the common preimage for the primitive rhombohedral unit cells of the P, D and G surfaces. The dark and light triangles are $[\star{\tt 246}]$ domains – there are 96 such triangles in the dodecagonal translation unit. The translations that pair opposite sides of the dodecagon generate an irregular (12, 12) tiling of the hyperbolic plane, illustrated to the right. Eleven additional dodecagons (alternating pale and bright blue) meet at each vertex of the central triangulated dodecagon.

FOUNDATIONS
ADVANCES

ISSN: 2053-2733

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

doi:10.1107/S0108767308040592

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