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PARALLELOGON

Parallelogon

Polygon able to tessellate edge-to-edge, without rotation

In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted)

Parallelogon

Hexagon

Shape with six sides

g2 hexagons, with opposite sides parallel are also called hexagonal parallelogons. Each subgroup symmetry allows one or more degrees of freedom for irregular

Hexagon

Conway criterion

Rule from the theory of the tiling of the plane

rotations—about the midpoints of two adjacent edges in the case of a hexagonal parallelogon, and about the midpoint of an edge and one of its vertices in the case

Conway criterion

Conway_criterion

Parallelogram

Quadrilateral with two pairs of parallel sides

parallelepiped is a three-dimensional figure whose six faces are parallelograms. parallelogon, generalisation encompassing hexagons as well as quadrilaterals zonogon

Parallelogram

Parallelotope

Topics referred to by the same term

parallelepiped and parallelogram A generalization of a parallelohedron and parallelogon, this includes all parallelohedra in the first sense Zonotope This disambiguation

Parallelotope

Point reflection

Geometric symmetry operation

2D examples Hexagonal parallelogon Octagon

Point reflection

Point_reflection

Hexagonal tiling

Regular tiling of a two-dimensional space

represent the lattice positions. Single-color (1-tile) lattices are parallelogon hexagons. Other isohedrally-tiled topological hexagonal tilings are seen

Hexagonal tiling

Hexagonal_tiling

Triangular tiling

Regular tiling of the plane

plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees

Triangular tiling

Triangular_tiling

List of Greek and Latin roots in English/A–G

All Latin and Greek roots beginning with G

ἀλλήλων (allḗlōn) allele, allelomorph, allelotaxis, parallel, parallelism, parallelogon, parallelogram alph- A, a Greek Α, α, ἄλφα (álpha) alphabet, alphabetic

List of Greek and Latin roots in English/A–G

List_of_Greek_and_Latin_roots_in_English/A–G

Auxetics

Materials that have a negative Poisson's ratio

products. Acoustic metamaterial Mechanical metamaterial Metamaterial Parallelogon Zetix, a type of commercially manufactured auxetic material Lakes, R

Auxetics

Parallelohedron

Polyhedron that tiles space by translation

The three-dimensional parallelohedra are analogous to two-dimensional parallelogons and higher-dimensional parallelotopes. A parallelohedron is defined

Parallelohedron

Tilings and patterns

Mathematics book

triangular tiling, quadrilteral tiling, pentagonal tiling, hexagonal tiling, parallelogon, §9.2 non-convex polygon tilings, §9.3 anisohedral tiling, §9.4 polyomino

Tilings and patterns

Tilings_and_patterns

Zonogon

Convex polygon with pairs of equal, parallel sides

six-sided zonogons are parallelogons, able to tile the plane by translated copies of themselves, and all convex parallelogons have this form. Every 2

Zonogon

List of Greek and Latin roots in English/A

All Latin and Greek roots beginning with A

ἀλλήλων (allḗlōn) allele, allelomorph, allelotaxis, parallel, parallelism, parallelogon, parallelogram alph- A, a Greek Α, α, ἄλφα (álpha) alphabet, alphabetic

List of Greek and Latin roots in English/A

List_of_Greek_and_Latin_roots_in_English/A