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Rhombille tiling, the Glossary

In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane.^[1]

54 relations: Ambiguous image, Angle, Aperiodic tiling, Axonometric projection, Billiard-ball computer, Block cellular automaton, Condensed matter physics, Convex and Concave, Crystal, Delos, Diatomic molecule, Dual polyhedron, Edge tessellation, English heraldry, Euclidean plane, Euclidean tilings by convex regular polygons, Geometry, Hexagon, Hexagonal tiling, Integer lattice, Ising model, Isohedral figure, Isometric projection, Isotoxal figure, List of Euclidean uniform tilings, List of regular polytope compounds, M. C. Escher, Metamorphosis I, Metamorphosis II, Metamorphosis III, Miura fold, Mosaic, Necker cube, Parquet, Partial cube, Penrose tiling, Percolation theory, Polyiamond, Q*bert, Quilting, Quilts of the Underground Railroad, Rhombus, Siena Cathedral, Spin (physics), Tallinn, Taschen, Taxicab geometry, Tessellation, Trihexagonal tiling, Turing completeness, ... Expand index (4 more) »
Euclidean tilings
Isohedral tilings
Isotoxal tilings
Quasiregular polyhedra

Ambiguous image

Ambiguous images or reversible figures are visual forms that create ambiguity by exploiting graphical similarities and other properties of visual system interpretation between two or more distinct image forms.

See Rhombille tiling and Ambiguous image

Angle

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

See Rhombille tiling and Angle

Aperiodic tiling

An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches.

See Rhombille tiling and Aperiodic tiling

Axonometric projection

Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the object is rotated around one or more of its axes to reveal multiple sides.

See Rhombille tiling and Axonometric projection

Billiard-ball computer

A billiard-ball computer, a type of conservative logic circuit, is an idealized model of a reversible mechanical computer based on Newtonian dynamics, proposed in 1982 by Edward Fredkin and Tommaso Toffoli.

See Rhombille tiling and Billiard-ball computer

Block cellular automaton

A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping blocks (with different partitions at different time steps) and the transition rule is applied to a whole block at a time rather than a single cell.

See Rhombille tiling and Block cellular automaton

Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons.

See Rhombille tiling and Condensed matter physics

Convex and Concave

Convex and Concave is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1955.

See Rhombille tiling and Convex and Concave

Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

See Rhombille tiling and Crystal

Delos

Delos (Δήλος; Δῆλος, Δᾶλος), is a small Greek island near Mykonos, close to the centre of the Cyclades archipelago.

See Rhombille tiling and Delos

Diatomic molecule

Diatomic molecules are molecules composed of only two atoms, of the same or different chemical elements.

See Rhombille tiling and Diatomic molecule

Dual polyhedron

In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

See Rhombille tiling and Dual polyhedron

Edge tessellation

In geometry, an edge tessellation is a partition of the plane into non-overlapping polygons (a tessellation) with the property that the reflection of any of these polygons across any of its edges is another polygon in the tessellation.

See Rhombille tiling and Edge tessellation

English heraldry

English heraldry is the form of coats of arms and other heraldic bearings and insignia used in England.

See Rhombille tiling and English heraldry

Euclidean plane

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.

See Rhombille tiling and Euclidean plane

Euclidean tilings by convex regular polygons

Euclidean plane tilings by convex regular polygons have been widely used since antiquity.

See Rhombille tiling and Euclidean tilings by convex regular polygons

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Rhombille tiling and Geometry

Hexagon

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon.

See Rhombille tiling and Hexagon

Hexagonal tiling

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. Rhombille tiling and hexagonal tiling are Euclidean tilings and isohedral tilings.

See Rhombille tiling and Hexagonal tiling

Integer lattice

In mathematics, the -dimensional integer lattice (or cubic lattice), denoted, is the lattice in the Euclidean space whose lattice points are n-tuples of integers.

See Rhombille tiling and Integer lattice

Ising model

The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics.

See Rhombille tiling and Ising model

Isohedral figure

In geometry, a tessellation of dimension (a plane tiling) or higher, or a polytope of dimension (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same.

See Rhombille tiling and Isohedral figure

Isometric projection

Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings.

See Rhombille tiling and Isometric projection

Isotoxal figure

In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal or edge-transitive if its symmetries act transitively on its edges.

See Rhombille tiling and Isotoxal figure

List of Euclidean uniform tilings

This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. Rhombille tiling and List of Euclidean uniform tilings are Euclidean tilings.

See Rhombille tiling and List of Euclidean uniform tilings

List of regular polytope compounds

This article lists the regular polytope compounds in Euclidean, spherical and hyperbolic spaces.

See Rhombille tiling and List of regular polytope compounds

M. C. Escher

Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics.

See Rhombille tiling and M. C. Escher

Metamorphosis I is a woodcut print by the Dutch artist M. C. Escher which was first printed in May, 1937.

See Rhombille tiling and Metamorphosis I

Metamorphosis II is a woodcut print by the Dutch artist M. C. Escher.

See Rhombille tiling and Metamorphosis II

Metamorphosis III is a woodcut print by the Dutch artist M. C. Escher created during 1967 and 1968.

See Rhombille tiling and Metamorphosis III

Miura fold

The is a method of folding a flat surface such as a sheet of paper into a smaller area.

See Rhombille tiling and Miura fold

Mosaic

A mosaic is a pattern or image made of small regular or irregular pieces of colored stone, glass or ceramic, held in place by plaster/mortar, and covering a surface.

See Rhombille tiling and Mosaic

Necker cube

The Necker cube is an optical illusion that was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker.

See Rhombille tiling and Necker cube

Parquet

Parquet (French for "a small compartment") is a geometric mosaic of wood pieces used for decorative effect in flooring.

See Rhombille tiling and Parquet

Partial cube

In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube.

See Rhombille tiling and Partial cube

Penrose tiling

A Penrose tiling is an example of an aperiodic tiling.

See Rhombille tiling and Penrose tiling

Percolation theory

In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added.

See Rhombille tiling and Percolation theory

Polyiamond

A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino) is a polyform whose base form is an equilateral triangle.

See Rhombille tiling and Polyiamond

Q*bert

Q*bert is an arcade video game developed and published for the North American market by Gottlieb in 1982.

See Rhombille tiling and Q*bert

Quilting

Quilting is the process of joining a minimum of three layers of fabric together either through stitching manually using a needle and thread, or mechanically with a sewing machine or specialised longarm quilting system.

See Rhombille tiling and Quilting

Quilts of the Underground Railroad

Quilts of the Underground Railroad describes a controversial belief that quilts were used to communicate information to African slaves about how to escape to freedom via the Underground Railroad.

See Rhombille tiling and Quilts of the Underground Railroad

Rhombus

In plane Euclidean geometry, a rhombus (rhombi or rhombuses) is a quadrilateral whose four sides all have the same length.

See Rhombille tiling and Rhombus

Siena Cathedral

Siena Cathedral (Duomo di Siena) is a medieval church in Siena, Italy, dedicated from its earliest days as a Roman Catholic Marian church, and now dedicated to the Assumption of Mary.

See Rhombille tiling and Siena Cathedral

Spin (physics)

Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms.

See Rhombille tiling and Spin (physics)

Tallinn

Tallinn is the capital and most populous city of Estonia.

See Rhombille tiling and Tallinn

Taschen

Taschen is a luxury art book publisher founded in 1980 by Benedikt Taschen in Cologne, Germany.

See Rhombille tiling and Taschen

Taxicab geometry

Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.

See Rhombille tiling and Taxicab geometry

Tessellation

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps.

See Rhombille tiling and Tessellation

Trihexagonal tiling

In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. Rhombille tiling and trihexagonal tiling are Euclidean tilings, isotoxal tilings and Quasiregular polyhedra.

See Rhombille tiling and Trihexagonal tiling

Turing completeness

In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing).

See Rhombille tiling and Turing completeness

References

[1] https://en.wikipedia.org/wiki/Rhombille_tiling

Also known as Cubic tiling, Quasiregular rhombic tiling, Rhombic tiling, Rhombille, Tumbling block tiling, Tumbling blocks.

, Underground Railroad, Uniform tiling, Unit distance graph, Vertex configuration.

Rhombille tiling, the Glossary

Table of Contents

See also

Euclidean tilings

Isohedral tilings

Isotoxal tilings

Quasiregular polyhedra

References