• Source: Truncated order-8 octagonal tiling

In geometry, the truncated order-8 octagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{8,8}.




Uniform colorings


This tiling can also be constructed in *884 symmetry with 3 colors of faces:




Related polyhedra and tiling






= Symmetry

=
The dual of the tiling represents the fundamental domains of (*884) orbifold symmetry. From [(8,8,4)] (*884) symmetry, there are 15 small index subgroup (11 unique) by mirror removal and alternation operators. Mirrors can be removed if its branch orders are all even, and cuts neighboring branch orders in half. Removing two mirrors leaves a half-order gyration point where the removed mirrors met. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors. The symmetry can be doubled to 882 symmetry by adding a bisecting mirror across the fundamental domains. The subgroup index-8 group, [(1+,8,1+,8,1+,4)] (442442) is the commutator subgroup of [(8,8,4)].




References


John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, 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


Square tiling
Tilings of regular polygons
List of uniform planar tilings
List of regular polytopes




External links


Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
Hyperbolic and Spherical Tiling Gallery
KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
Hyperbolic Planar Tessellations, Don Hatch

Kata Kunci Pencarian:

• Truncated order-8 octagonal tiling
• Truncated order-8 triangular tiling
• Truncated octagonal tiling
• Truncated order-4 octagonal tiling
• Truncated order-6 octagonal tiling
• Octagonal tiling
• Truncated square tiling
• Truncated cuboctahedron
• Truncated order-8 hexagonal tiling
• Truncated hexagonal tiling