"Tumbling blocks" redirects here. For other uses, see Jacob's ladder (toy).
Rhombille tiling
Type
Laves tiling
Faces
60°–120° rhombus
Coxeter diagram
Symmetry group
p6m, [6,3], *632 p3m1, [3[3]], *333
Rotation group
p6, [6,3]+, (632) p3, [3[3]]+, (333)
Dual polyhedron
Trihexagonal tiling
Face configuration
V3.6.3.6
Properties
edge-transitive, face-transitive
In geometry, the rhombille tiling,[1] also known as tumbling blocks,[2]reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets of six rhombi meet at their 60° angles.
^Conway, John; Burgiel, Heidi; Goodman-Strauss, Chaim (2008), "Chapter 21: Naming Archimedean and Catalan polyhedra and tilings", The Symmetries of Things, AK Peters, p. 288, ISBN 978-1-56881-220-5.
^Cite error: The named reference tumble1 was invoked but never defined (see the help page).
six rhombi meet at their 60° angles. The rhombilletiling can be seen as a subdivision of a hexagonal tiling with each hexagon divided into three rhombi...
arrangement of lines. Its dual is the rhombilletiling. This pattern, and its place in the classification of uniform tilings, was already known to Johannes Kepler...
truncated trihexagonal tiling has three related 2-uniform tilings, one being a 2-uniform coloring of the semiregular rhombitrihexagonal tiling. The first dissects...
lattice. Identical rhombi can tile the 2D plane in three different ways, including, for the 60° rhombus, the rhombilletiling. Three-dimensional analogues...
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex...
topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter...
In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal (from Greek τόξον 'arc') or edge-transitive if its symmetries...
dissected into 3 rhombi around its center. These rhombi are the tiles of a rhombille. The collections of the Louvre include a die in the shape of a rhombic...
In geometry, the pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{6,5} or t1{6,5}. John H. Conway, Heidi...
attempt to tile a plane with as many polyiamonds as possible, subject to the game rules. Triangular tilingRhombilletiling Sphinx tiling Weisstein, Eric...
continues as the trihexagonal tiling, vertex figure (3.6)2 - a quasiregular tiling based on the triangular tiling and hexagonal tiling. The checkerboard pattern...
sometimes useful in some roleplaying games or other places. Golden rhombus Rhombilletiling Truncated rhombic triacontahedron Stephen Wolfram, "[1]" from Wolfram...
tiling) this produces the rhombilletiling. However, for more families of lines this construction produces aperiodic tilings. In particular, for five families...
duals: There are at least 5 polygonal tilings of the Euclidean plane that are isotoxal. (The self-dual square tiling recreates itself in all four forms.)...
through the tiling, so each of these four tessellations can alternatively be viewed as an arrangement of lines. In the second four, each tile has at least...
tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{4,7}. Wikimedia Commons has media related to Uniform tiling 4-7-4-7...
can be said to have a (regular) pentagonal vertex arrangement. Infinite tilings can also share common vertex arrangements. For example, this triangular...
the Percolation Thresholds of a Three-Dimensional (Icosahedral) Penrose Tiling by the Cubic Approximant Method". Crystallography Reports. 50 (6): 938–948...
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