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TRUNCATED TRIHEXAGONAL-TILING

  • Truncated trihexagonal tiling
  • Uniform tiling of the Euclidean plane

    In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane. There are one square, one hexagon, and one

    Truncated trihexagonal tiling

    Truncated trihexagonal tiling

    Truncated_trihexagonal_tiling

  • Trihexagonal tiling
  • Tiling of a plane by regular hexagons and equilateral triangles

    In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. It consists of equilateral triangles and

    Trihexagonal tiling

    Trihexagonal tiling

    Trihexagonal_tiling

  • Snub trihexagonal tiling
  • Semiregular tiling of the Euclidean plane

    In geometry, the snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon

    Snub trihexagonal tiling

    Snub trihexagonal tiling

    Snub_trihexagonal_tiling

  • Rhombitrihexagonal tiling
  • Semiregular tiling of the Euclidean plane

    dissected into six triangles. The rhombitrihexagonal tiling is also related to the truncated trihexagonal tiling by replacing some of the hexagons and surrounding

    Rhombitrihexagonal tiling

    Rhombitrihexagonal tiling

    Rhombitrihexagonal_tiling

  • List of Euclidean uniform tilings
  •   Truncated trihexagonal tiling – 1 coloring, wythoffian   Snub hexagonal tiling – 1 coloring, alternated wythoffian   Elongated triangular tiling – 1

    List of Euclidean uniform tilings

    List of Euclidean uniform tilings

    List_of_Euclidean_uniform_tilings

  • Triangular prismatic honeycomb
  • trihexagonal tiling extruded into prisms. It is one of 28 convex uniform honeycombs. The truncated hexagonal prismatic honeycomb or tomo-trihexagonal

    Triangular prismatic honeycomb

    Triangular prismatic honeycomb

    Triangular_prismatic_honeycomb

  • Triangular tiling honeycomb
  • 3]. The cantitruncated triangular tiling honeycomb, , has truncated trihexagonal tiling, truncated hexagonal tiling, and triangular prism cells, with

    Triangular tiling honeycomb

    Triangular tiling honeycomb

    Triangular_tiling_honeycomb

  • Hexagonal tiling honeycomb
  • Regular paracompact honeycomb

    tetrahedron, truncated trihexagonal tiling, and triangular prism cells, with a mirrored sphenoid vertex figure. The runcinated hexagonal tiling honeycomb

    Hexagonal tiling honeycomb

    Hexagonal tiling honeycomb

    Hexagonal_tiling_honeycomb

  • Euclidean tilings by convex regular polygons
  • Subdivision of the plane into polygons that are all regular

    {\displaystyle 2+{\sqrt {3}}} . This can similarly be done with the truncated trihexagonal tiling as a basis, with corresponding dilation of 3 + 3 {\displaystyle

    Euclidean tilings by convex regular polygons

    Euclidean tilings by convex regular polygons

    Euclidean_tilings_by_convex_regular_polygons

  • Order-6 hexagonal tiling honeycomb
  • order-6 hexagonal tiling honeycomb, h2,3{6,3,6}, , or , contains truncated trihexagonal tiling, truncated hexagonal tiling, trihexagonal tiling, and triangular

    Order-6 hexagonal tiling honeycomb

    Order-6 hexagonal tiling honeycomb

    Order-6_hexagonal_tiling_honeycomb

  • Order-4 hexagonal tiling honeycomb
  • order-4 hexagonal tiling honeycomb, q{6,3,4}, or , is composed of triangular tiling, trihexagonal tiling, tetrahedron, and truncated tetrahedron cells

    Order-4 hexagonal tiling honeycomb

    Order-4 hexagonal tiling honeycomb

    Order-4_hexagonal_tiling_honeycomb

  • Conway polyhedron notation
  • Method of describing higher-order polyhedra

    Trihexagonal tiling aH = aΔ Truncated hexagonal tiling tH Rhombitrihexagonal tiling eH = eΔ Truncated trihexagonal tiling bH = bΔ Snub trihexagonal tiling

    Conway polyhedron notation

    Conway polyhedron notation

    Conway_polyhedron_notation

  • Uniform tilings in hyperbolic plane
  • Symmetric subdivision in hyperbolic geometry

    hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic

    Uniform tilings in hyperbolic plane

    Uniform_tilings_in_hyperbolic_plane

  • Truncated hexagonal tiling
  • Semiregular tiling of a plane

    In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each

    Truncated hexagonal tiling

    Truncated hexagonal tiling

    Truncated_hexagonal_tiling

  • 12 (number)
  • Natural number

    can uniformly tile the plane alongside other regular polygons, as with the truncated hexagonal tiling or the truncated trihexagonal tiling. A regular dodecahedron

    12 (number)

    12_(number)

  • Order-5 hexagonal tiling honeycomb
  • icosahedron, truncated trihexagonal tiling, and pentagonal prism facets, with a mirrored sphenoid vertex figure. The runcinated order-5 hexagonal tiling honeycomb

    Order-5 hexagonal tiling honeycomb

    Order-5 hexagonal tiling honeycomb

    Order-5_hexagonal_tiling_honeycomb

  • Octadecagon
  • Polygon with 18 edges

    tiling mixes in nonagons and octagonal gaps. The first tiling is related to a truncated hexagonal tiling, and the second the truncated trihexagonal tiling

    Octadecagon

    Octadecagon

    Octadecagon

  • Circle packing
  • Field of geometry closely arranging circles on a plane

    3-uniform packings. The truncated trihexagonal tiling with both types of gaps can be filled as a 4-uniform packing. The snub hexagonal tiling has two mirror-image

    Circle packing

    Circle packing

    Circle_packing

  • Alternated hexagonal tiling honeycomb
  • composed of octahedron, truncated tetrahedron, and trihexagonal tiling facets, with a wedge vertex figure. The runcic hexagonal tiling honeycomb, h3{6,3,3}

    Alternated hexagonal tiling honeycomb

    Alternated_hexagonal_tiling_honeycomb

  • List of mathematical shapes
  • Snub square tiling Trihexagonal tiling Truncated hexagonal tiling Rhombitrihexagonal tiling Truncated trihexagonal tiling Snub hexagonal tiling Elongated

    List of mathematical shapes

    List_of_mathematical_shapes

  • Vertex configuration
  • Notation for a polyhedron's vertex figure

    Semiregular tilings: Truncated hexagonal tiling: 3.12.12 Truncated trihexagonal tiling: 4.6.12 Truncated square tiling: 4.8.8 Quadruples Platonic solids: Octahedron:

    Vertex configuration

    Vertex configuration

    Vertex_configuration

  • List of polygons, polyhedra and polytopes
  • Snub square tiling Trihexagonal tiling Truncated hexagonal tiling Rhombitrihexagonal tiling Truncated trihexagonal tiling Snub hexagonal tiling Elongated

    List of polygons, polyhedra and polytopes

    List_of_polygons,_polyhedra_and_polytopes

  • List of tessellations
  • Tessellation Uniform tiling Convex uniform honeycombs List of k-uniform tilings List of Euclidean uniform tilings Uniform tilings in hyperbolic plane Weisstein

    List of tessellations

    List_of_tessellations

  • Order-6 tetrahedral honeycomb
  • Poincaré disk model The truncated order-6 tetrahedral honeycomb, t0,1{3,3,6} has truncated tetrahedron and triangular tiling cells arranged in a hexagonal

    Order-6 tetrahedral honeycomb

    Order-6 tetrahedral honeycomb

    Order-6_tetrahedral_honeycomb

  • 3-4-6-12 tiling
  • Uniform Tiling

    tiling has right triangle and kite faces, defined by face configurations: V3.4.6.4 and V4.6.12, and can be seen combining the deltoidal trihexagonal tiling

    3-4-6-12 tiling

    3-4-6-12 tiling

    3-4-6-12_tiling

  • Quasiregular polyhedron
  • Polyhedron with two kinds of faces

    parent, truncating the vertices fully, until each original edge is reduced to its midpoint. This sequence continues as the trihexagonal tiling, vertex

    Quasiregular polyhedron

    Quasiregular_polyhedron

  • Octahedral-hexagonal tiling honeycomb
  • octahedron-hexagonal tiling honeycomb is a paracompact uniform honeycomb, constructed from octahedron, hexagonal tiling, and trihexagonal tiling cells, in a rhombicuboctahedron

    Octahedral-hexagonal tiling honeycomb

    Octahedral-hexagonal_tiling_honeycomb

  • Planigon
  • Convex polygon which can tile the plane by itself

    Laves tilings are unique except for the square tiling (1 degree of freedom), barn pentagonal tiling (1 degree of freedom), and hexagonal tiling (2 degrees

    Planigon

    Planigon

    Planigon

  • Harmonice Mundi
  • 1619 book by Johannes Kepler

    terms of basic triangles. The book features illustrations of solids and tiling patterns, some of which are related to the golden ratio. While medieval

    Harmonice Mundi

    Harmonice Mundi

    Harmonice_Mundi

  • Cyclotruncated simplicial honeycomb
  • colored line segments. In 2-dimensions, the honeycomb represents the trihexagonal tiling, with Coxeter graph . In 3-dimensions it represents the quarter cubic

    Cyclotruncated simplicial honeycomb

    Cyclotruncated simplicial honeycomb

    Cyclotruncated_simplicial_honeycomb

  • Rectification (geometry)
  • Operation in Euclidean geometry

    square tiling {4,4} will turn into another square tiling {4,4} under a rectification operation. Rectification is the final point of a truncation process

    Rectification (geometry)

    Rectification (geometry)

    Rectification_(geometry)

  • Equilateral triangle
  • Shape with three equal sides

    hexagonal tiling, rhombitrihexagonal tiling, trihexagonal tiling, snub square tiling, and snub hexagonal tiling are all semi-regular tessellations constructed

    Equilateral triangle

    Equilateral triangle

    Equilateral_triangle

  • Quarter cubic honeycomb
  • central inversion. In each trihexagonal tiling, half of the triangles belong to tetrahedra, and half belong to truncated tetrahedra. These slab layers

    Quarter cubic honeycomb

    Quarter cubic honeycomb

    Quarter_cubic_honeycomb

  • Order-6 dodecahedral honeycomb
  • Regular geometrical object in hyperbolic space

    pentaapeirogonal tiling, r{5,∞} with pentagon and apeirogonal faces. The truncated order-6 dodecahedral honeycomb, t0,1{5,3,6} has truncated dodecahedron

    Order-6 dodecahedral honeycomb

    Order-6 dodecahedral honeycomb

    Order-6_dodecahedral_honeycomb

  • Isotoxal figure
  • Polytope or tiling with one type of edge

    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

    Isotoxal figure

    Isotoxal_figure

  • Tilings and patterns
  • Mathematics book

    topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter

    Tilings and patterns

    Tilings_and_patterns

  • Wallpaper group
  • Classification of a two-dimensional repetitive pattern

    Triangular tiling (ignoring colors: p6m) Hexagonal tiling (ignoring colors: p6m) Truncated hexagonal tiling (ignoring colors: p6m) Persian glazed tile (ignoring

    Wallpaper group

    Wallpaper group

    Wallpaper_group

  • Uniform honeycombs in hyperbolic space
  • Tiling of hyperbolic 3-space by uniform polyhedra

    paracompact for p=6 (with a snub trihexagonal tiling as the vertex figure), and hypercompact for p>6. Again, the truncated and rectified versions of these

    Uniform honeycombs in hyperbolic space

    Uniform honeycombs in hyperbolic space

    Uniform_honeycombs_in_hyperbolic_space

  • Uniform honeycomb
  • Isogonal honeycomb of uniform polytope facets

    face at each edge radiating from the vertex. Uniform tiling List of uniform tilings Uniform tilings in hyperbolic plane Honeycomb (geometry) Wythoff construction

    Uniform honeycomb

    Uniform_honeycomb

  • Polytope compound
  • 3D shape made of polyhedra sharing a common center

    dual triangular tiling, which shares its edges with the deltoidal trihexagonal tiling. The Euclidean compounds of two hypercubic honeycombs are both regular

    Polytope compound

    Polytope_compound

  • Convex uniform honeycomb
  • Spatial tiling of convex uniform polyhedra

    unique honeycombs from the square tiling, but all 6 tiling truncations are listed below for completeness, and tiling images are shown by colors corresponding

    Convex uniform honeycomb

    Convex uniform honeycomb

    Convex_uniform_honeycomb

  • Arrangement of lines
  • Subdivision of the plane by lines

    simplicial rather than simple. Its dual is the truncated square tiling. Similarly, the triangular tiling is an infinite simplicial line arrangement with

    Arrangement of lines

    Arrangement of lines

    Arrangement_of_lines

  • Percolation threshold
  • Threshold of percolation theory models

    the Percolation Thresholds of a Three-Dimensional (Icosahedral) Penrose Tiling by the Cubic Approximant Method". Crystallography Reports. 50 (6): 938–948

    Percolation threshold

    Percolation threshold

    Percolation_threshold

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  • Court
  • Surname or Lastname

    English and French

    Court

    English and French : topographic name from Middle English, Old French court(e), curt ‘court’ (Latin cohors, genitive cohortis, ‘yard’, ‘enclosure’). This word was used primarily with reference to the residence of the lord of a manor, and the surname is usually an occupational name for someone employed at a manorial court.English : nickname from Old French, Middle English curt ‘short’, ‘small’ (Latin curtus ‘curtailed’, ‘truncated’, ‘cut short’, ‘broken off’).Irish : reduced form of McCourt.

    Court

  • Myatt
  • Surname or Lastname

    English (chiefly West Midlands)

    Myatt

    English (chiefly West Midlands) : from the Middle English personal name Myat, formed from My, a truncated version of Mihel (an Old French form of Michael) + the diminutive suffix -at (from Old French -et, crossed with the originally pejorative Old French -ard).

    Myatt

  • Aliff
  • Surname or Lastname

    English

    Aliff

    English : variant of Ayliff(e), which is from a Middle English personal name. In most cases, this is Old Norse Eilífr ‘eternal life’, but it could also have absorbed the female name Ayleve (Old English Æ{dh}elgifu ‘noble gift’). It could also have absorbed a truncated form of Irish McAuliffe.

    Aliff

  • Teeling
  • Surname or Lastname

    English and Irish

    Teeling

    English and Irish : unexplained; most probably a habitational name from a lost or unidentified place somewhere in South Wales or southern England. This name was established in County Meath, Ireland, soon after the Anglo-Norman invasion of the 12th century.Dutch : unexplained.Probably a respelling of German Tiling, a patronymic form of Thiel.

    Teeling

  • Hartell
  • Surname or Lastname

    English (West Midlands)

    Hartell

    English (West Midlands) : habitational name from any of the places called Harthill, named with Old English heorot ‘hart’ + hyll ‘hill’. There are several places of this name, for example in Cheshire, Derbyshire, and South Yorkshire, but apparently none in the West Midlands. It is also possible that the surname represents a truncated derivative of Hartlebury in Worcestershire. This place name derives from the Old English personal name Heortla + Old English burh ‘fort’.German : Americanized spelling of Hartel or Härtel.

    Hartell

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TRUNCATED TRIHEXAGONAL-TILING

  • Truncated
  • a.

    Cut off; cut short; maimed.

  • Titler
  • n.

    A large truncated cone of refined sugar.

  • Truncated
  • a.

    Replaced, or cut off, by a plane, especially when equally inclined to the adjoining faces; as, a truncated edge.

  • Truncate
  • v. t.

    To cut off; to lop; to maim.

  • Dihexagonal
  • a.

    Having twelve similar faces; as, a dihexagonal prism.

  • Tunicated
  • a.

    Covered with a tunic; covered or coated with layers; as, a tunicated bulb.

  • Dihexagonal
  • a.

    Consisting of two hexagonal parts united; thus, a dihexagonal pyramid is composed of two hexagonal pyramids placed base to base.

  • Fron'tated
  • a.

    Growing broader and broader, as a leaf; truncate.

  • Stubbed
  • a.

    Reduced to a stub; short and thick, like something truncated; blunt; obtuse.

  • Emarginated
  • a.

    Having the edges truncated.

  • Truncation
  • n.

    The state of being truncated.

  • Pylon
  • n.

    A low tower, having a truncated pyramidal form, and flanking an ancient Egyptian gateway.

  • Tunicated
  • a.

    Having a tunic, or mantle; of or pertaining to the Tunicata.

  • Truncated
  • imp. & p. p.

    of Truncate

  • Tunicate
  • a.

    Alt. of Tunicated

  • Trunk
  • v. t.

    To lop off; to curtail; to truncate; to maim.

  • Truncate
  • a.

    Appearing as if cut off at the tip; as, a truncate leaf or feather.

  • Truncating
  • p. pr. & vb. n.

    of Truncate

  • Truncated
  • a.

    Lacking the apex; -- said of certain spiral shells in which the apex naturally drops off.

  • Tunicated
  • a.

    Having each joint buried in the preceding funnel-shaped one, as in certain antennae of insects.