Order-6 pentagonal tiling

Uniform coloring

This regular tiling can also be constructed from [(5,5,3)] symmetry alternating two colors of pentagons, represented by t1(5,5,3).

Symmetry

This tiling represents a hyperbolic kaleidoscope of 6 mirrors defining a regular hexagon fundamental domain, and 5 mirrors meeting at a point. This symmetry by orbifold notation is called *33333 with 5 order-3 mirror intersections.


This tiling is topologically related as a part of sequence of regular tilings with order-6 vertices with Schläfli symbol {n,6}, and Coxeter diagram , progressing to infinity.

Regular tilings {n,6}
Spherical Euclidean Hyperbolic tilings

{2,6}

{3,6}

{4,6}

{5,6}

{6,6}

{7,6}

{8,6}
...
{,6}
Uniform hexagonal/pentagonal tilings
Symmetry: [6,5], (*652) [6,5]+, (652) [6,5+], (5*3) [1+,6,5], (*553)
{6,5} t{6,5} r{6,5} 2t{6,5}=t{5,6} 2r{6,5}={5,6} rr{6,5} tr{6,5} sr{6,5} s{5,6} h{6,5}
Uniform duals
V65 V5.12.12 V5.6.5.6 V6.10.10 V56 V4.5.4.6 V4.10.12 V3.3.5.3.6 V3.3.3.5.3.5 V(3.5)5

References

    • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
    • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

    See also

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