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==2D with 1D surface== * [[Convex polygon]] * [[Concave polygon]] * [[Constructible polygon]] * [[Cyclic polygon]] * [[Equiangular polygon]] * [[Equilateral polygon]] * [[Regular polygon]] * [[Penrose tile]] * [[Polyform]] * [[Balbis]] *[[Gnomon (figure)|Gnomon]] *[[Golygon]] * [[Star (polygon)|Star]] without crossing lines * [[Star polygon]] ** [[Hexagram]] *** [[Star of David]] ** [[Heptagram]] ** [[Octagram]] *** [[Star of Lakshmi]] ** [[Decagram (geometry)|Decagram]] ** [[Pentagram]] Polygons named for their number of sides {{div col|colwidth=18em}} * [[Monogon]] — 1 sided * [[Digon]] — 2 sided * [[Triangle]] ** [[Acute triangle]] ** [[Equilateral triangle]] ** [[Isosceles triangle]] ** [[Obtuse triangle]] ** [[Rational triangle]] ** [[Right triangle]] *** [[30-60-90 triangle]] *** [[Isosceles right triangle]] *** [[Kepler triangle]] ** [[Scalene triangle]] * [[Quadrilateral]] ** [[Cyclic quadrilateral]] ***[[Square (geometry)|square]] ** [[Kite (geometry)|kite]] ** [[Parallelogram]] *** [[Rhombus]] (equilateral parallelogram) **** [[Lozenge (shape)|Lozenge]] *** [[Rhomboid]] *** [[Rectangle]] **** [[Square (geometry)|square]] (regular quadrilateral) ** [[Tangential quadrilateral]] ** [[Trapezoid]] or trapezium *** [[Isosceles trapezoid]] * [[Pentagon]] ** [[Regular pentagon]] * [[Hexagon]] ** [[Lemoine hexagon]] * [[Heptagon]] * [[Octagon]] ** [[Regular octagon]] * [[Nonagon]] * [[Decagon]] ** [[Regular decagon]] * [[Hendecagon]] * [[Dodecagon]] *[[Triskaidecagon]] *[[Tetradecagon]] *[[Pentadecagon]] *[[Hexadecagon]] *[[Heptadecagon]] *[[Octadecagon]] *[[Enneadecagon]] * [[Icosagon]] *[[Triacontagon]] *[[Tetracontagon]] *[[Pentacontagon]] *[[Hexacontagon]] *[[Heptacontagon]] *[[Octacontagon]] *[[Enneacontagon]] *[[Hectogon]] *[[257-gon]] *[[Chiliagon]] *[[Myriagon]] *[[65537-gon]] *[[Megagon]] *[[Apeirogon]] {{div col end}} ===Tilings=== *[[List of uniform tilings]] *[[Uniform tilings in hyperbolic plane]] *[[Uniform tiling|Archimedean tiling]] **[[Square tiling]] **[[Triangular tiling]] **[[Hexagonal tiling]] **[[Truncated square tiling]] **[[Snub square tiling]] **[[Trihexagonal tiling]] **[[Truncated hexagonal tiling]] **[[Rhombitrihexagonal tiling]] **[[Truncated trihexagonal tiling]] **[[Snub hexagonal tiling]] **[[Elongated triangular tiling]] ===Uniform polyhedra=== {{main|Uniform polyhedron}} * [[Regular polyhedron]] ** [[Platonic solid]] *** [[Tetrahedron]] *** [[Cube]] *** [[Octahedron]] *** [[Dodecahedron]] *** [[Icosahedron]] ** [[Kepler–Poinsot polyhedron]] (regular star polyhedra) *** [[Great icosahedron]] *** [[Small stellated dodecahedron]] *** [[Great dodecahedron]] *** [[Great stellated dodecahedron]] ** Abstract regular polyhedra ([[Projective polyhedron]]) *** [[Hemicube (geometry)|Hemicube]] *** [[Hemi-octahedron]] *** [[Hemi-dodecahedron]] *** [[Hemi-icosahedron]] * [[Archimedean solid]] ** [[Truncated tetrahedron]] ** [[Cuboctahedron]] ** [[Truncated cube]] ** [[Truncated octahedron]] ** [[Rhombicuboctahedron]] ** [[Truncated cuboctahedron]] ** [[Snub cube]] ** [[Icosidodecahedron]] ** [[Truncated dodecahedron]] ** [[Truncated icosahedron]] ** [[Rhombicosidodecahedron]] ** [[Truncated icosidodecahedron]] ** [[Snub dodecahedron]] *[[Prismatic uniform polyhedron]] ** [[Prism (geometry)|Prism]] ** [[Antiprism]] <!-- Is there any point to listing the n-gonal prisms and antiprisms explicitly? --> * [[Uniform star polyhedron]] {{div col|colwidth=22em}} **[[Cubitruncated cuboctahedron]] **[[Cubohemioctahedron]] **[[Ditrigonal dodecadodecahedron]] **[[Dodecadodecahedron]] **[[Great cubicuboctahedron]] **[[Great dirhombicosidodecahedron]] **[[Great disnub dirhombidodecahedron]] **[[Great ditrigonal dodecicosidodecahedron]] **[[Great ditrigonal icosidodecahedron]] **[[Great dodecahemicosahedron]] **[[Great dodecahemidodecahedron]] **[[Great dodecicosahedron]] **[[Great dodecicosidodecahedron]] **[[Great icosicosidodecahedron]] **[[Great icosidodecahedron]] **[[Great icosihemidodecahedron]] **[[Great inverted snub icosidodecahedron]] **[[Great retrosnub icosidodecahedron]] **[[Great rhombidodecahedron]] **[[Great rhombihexahedron]] **[[Great snub dodecicosidodecahedron]] **[[Great snub icosidodecahedron]] **[[Great stellated truncated dodecahedron]] **[[Great truncated cuboctahedron]] **[[Great truncated icosidodecahedron]] **[[Icosidodecadodecahedron]] **[[Icositruncated dodecadodecahedron]] **[[Inverted snub dodecadodecahedron]] **[[Nonconvex great rhombicosidodecahedron]] **[[Nonconvex great rhombicuboctahedron]] **[[Octahemioctahedron]] **[[Rhombicosahedron]] **[[Rhombidodecadodecahedron]] **[[Small cubicuboctahedron]] **[[Small ditrigonal dodecicosidodecahedron]] **[[Small ditrigonal icosidodecahedron]] **[[Small dodecahemicosahedron]] **[[Small dodecahemidodecahedron]] **[[Small dodecicosahedron]] **[[Small dodecicosidodecahedron]] **[[Small icosicosidodecahedron]] **[[Small icosihemidodecahedron]] **[[Small retrosnub icosicosidodecahedron]] **[[Small rhombidodecahedron]] **[[Small rhombihexahedron]] **[[Small snub icosicosidodecahedron]] **[[Small stellated truncated dodecahedron]] **[[Snub dodecadodecahedron]] **[[Snub icosidodecadodecahedron]] **[[Stellated truncated hexahedron]] **[[Tetrahemihexahedron]] **[[Truncated dodecadodecahedron]] **[[Truncated great dodecahedron]] **[[Truncated great icosahedron]] {{div col end}} ===Duals of uniform polyhedra=== * [[Catalan solid]] ** [[Triakis tetrahedron]] ** [[Rhombic dodecahedron]] ** [[Triakis octahedron]] ** [[Tetrakis hexahedron]] ** [[Deltoidal icositetrahedron]] ** [[Disdyakis dodecahedron]] ** [[Pentagonal icositetrahedron]] ** [[Rhombic triacontahedron]] ** [[Triakis icosahedron]] ** [[Pentakis dodecahedron]] ** [[Deltoidal hexecontahedron]] ** [[Disdyakis triacontahedron]] ** [[Pentagonal hexecontahedron]] {{div col|colwidth=22em}} * non-convex **[[Great complex icosidodecahedron]] **[[Great deltoidal hexecontahedron]] **[[Great deltoidal icositetrahedron]] **[[Great dirhombicosidodecacron]] **[[Great dirhombicosidodecahedron]] **[[Great disdyakis dodecahedron]] **[[Great disdyakis triacontahedron]] **[[Great disnub dirhombidodecacron]] **[[Great ditrigonal dodecacronic hexecontahedron]] **[[Great dodecacronic hexecontahedron]] **[[Great dodecahemicosacron]] **[[Great dodecicosacron]] **[[Great hexacronic icositetrahedron]] **[[Great hexagonal hexecontahedron]] **[[Great icosacronic hexecontahedron]] **[[Great icosihemidodecacron]] **[[Great inverted pentagonal hexecontahedron]] **[[Great pentagonal hexecontahedron]] **[[Great pentagrammic hexecontahedron]] **[[Great pentakis dodecahedron]] **[[Great rhombic triacontahedron]] **[[Great rhombidodecacron]] **[[Great rhombihexacron]] **[[Great stellapentakis dodecahedron]] **[[Great triakis icosahedron]] **[[Great triakis octahedron]] **[[Great triambic icosahedron]] **[[Medial deltoidal hexecontahedron]] **[[Medial disdyakis triacontahedron]] **[[Medial hexagonal hexecontahedron]] **[[Medial icosacronic hexecontahedron]] **[[Medial inverted pentagonal hexecontahedron]] **[[Medial pentagonal hexecontahedron]] **[[Medial rhombic triacontahedron]] **[[Hexahemioctacron]] **[[Hemipolyhedron]] **[[Octahemioctacron]] **[[Rhombicosacron]] **[[Small complex icosidodecahedron]] **[[Small ditrigonal dodecacronic hexecontahedron]] **[[Small dodecacronic hexecontahedron]] **[[Small dodecahemicosacron]] **[[Small dodecahemidodecacron]] **[[Small dodecicosacron]] **[[Small hexacronic icositetrahedron]] **[[Small hexagonal hexecontahedron]] **[[Small hexagrammic hexecontahedron]] **[[Small icosacronic hexecontahedron]] **[[Small icosihemidodecacron]] **[[Small rhombidodecacron]] **[[Small rhombihexacron]] **[[Small stellapentakis dodecahedron]] **[[Small triambic icosahedron]] **[[Tetrahemihexacron]] {{div col end}} ===Johnson solids=== {{main|Johnson solid}} {{div col|colwidth=22em}} *[[Augmented dodecahedron]] *[[Augmented hexagonal prism]] *[[Augmented pentagonal prism]] *[[Augmented sphenocorona]] *[[Augmented triangular prism]] *[[Augmented tridiminished icosahedron]] *[[Augmented truncated cube]] *[[Augmented truncated dodecahedron]] *[[Augmented truncated tetrahedron]] *[[Biaugmented pentagonal prism]] *[[Biaugmented triangular prism]] *[[Biaugmented truncated cube]] *[[Bigyrate diminished rhombicosidodecahedron]] *[[Bilunabirotunda]] *[[Diminished rhombicosidodecahedron]] *[[Disphenocingulum]] *[[Elongated pentagonal bipyramid]] *[[Elongated pentagonal cupola]] *[[Elongated pentagonal gyrobicupola]] *[[Elongated pentagonal gyrobirotunda]] *[[Elongated pentagonal gyrocupolarotunda]] *[[Elongated pentagonal orthobicupola]] *[[Elongated pentagonal orthobirotunda]] *[[Elongated pentagonal orthocupolarotunda]] *[[Elongated pentagonal pyramid]] *[[Elongated pentagonal rotunda]] *[[Elongated square bipyramid]] *[[Elongated square cupola]] *[[Elongated square gyrobicupola]] *[[Elongated square pyramid]] *[[Elongated triangular bipyramid]] *[[Elongated triangular cupola]] *[[Elongated triangular gyrobicupola]] *[[Elongated triangular orthobicupola]] *[[Elongated triangular pyramid]] *[[Gyrate bidiminished rhombicosidodecahedron]] *[[Gyrate rhombicosidodecahedron]] *[[Gyrobifastigium]] *[[Gyroelongated pentagonal bicupola]] *[[Gyroelongated pentagonal birotunda]] *[[Gyroelongated pentagonal cupola]] *[[Gyroelongated pentagonal cupolarotunda]] *[[Gyroelongated pentagonal pyramid]] *[[Gyroelongated pentagonal rotunda]] *[[Gyroelongated square bicupola]] *[[Gyroelongated square bipyramid]] *[[Gyroelongated square cupola]] *[[Gyroelongated square pyramid]] *[[Gyroelongated triangular bicupola]] *[[Gyroelongated triangular cupola]] *[[Hebesphenomegacorona]] *[[Metabiaugmented dodecahedron]] *[[Metabiaugmented hexagonal prism]] *[[Metabiaugmented truncated dodecahedron]] *[[Metabidiminished icosahedron]] *[[Metabidiminished rhombicosidodecahedron]] *[[Metabigyrate rhombicosidodecahedron]] *[[Metagyrate diminished rhombicosidodecahedron]] *[[Parabiaugmented dodecahedron]] *[[Parabiaugmented hexagonal prism]] *[[Parabiaugmented truncated dodecahedron]] *[[Parabidiminished rhombicosidodecahedron]] *[[Parabigyrate rhombicosidodecahedron]] *[[Paragyrate diminished rhombicosidodecahedron]] *[[Pentagonal bipyramid]] *[[Pentagonal cupola]] *[[Pentagonal gyrobicupola]] *[[Pentagonal gyrocupolarotunda]] *[[Pentagonal orthobicupola]] *[[Pentagonal orthobirotunda]] *[[Pentagonal orthocupolarotunda]] *[[Pentagonal pyramid]] *[[Pentagonal rotunda]] *[[Snub disphenoid]] *[[Snub square antiprism]] *[[Sphenocorona]] *[[Sphenomegacorona]] *[[Square cupola]] *[[Square gyrobicupola]] *[[Square orthobicupola]] *[[Square pyramid]] *[[Triangular bipyramid]] *[[Triangular cupola]] *[[Triangular hebesphenorotunda]] *[[Triangular orthobicupola]] *[[Triaugmented dodecahedron]] *[[Triaugmented hexagonal prism]] *[[Triaugmented triangular prism]] *[[Triaugmented truncated dodecahedron]] *[[Tridiminished icosahedron]] *[[Tridiminished rhombicosidodecahedron]] *[[Trigyrate rhombicosidodecahedron]] {{div col end}} ===Other nonuniform polyhedra=== *[[Pyramid (geometry)|Pyramid]] *[[Bipyramid]] *[[Disphenoid]] *[[Parallelepiped]] * [[Cuboid]] * [[Rhombohedron]] * [[Trapezohedron]] * [[Frustum]] * [[Trapezo-rhombic dodecahedron]] * [[Rhombo-hexagonal dodecahedron]] *[[Truncated trapezohedron]] *[[Deltahedron]] *[[Zonohedron]] *[[Prismatoid]] *[[Cupola (geometry)|Cupola]] *[[Bicupola]] ===Spherical polyhedra=== {{main|spherical polyhedron}} *[[Dihedron]] *[[Hosohedron]] ===Honeycombs=== ;[[Convex uniform honeycomb]] {{div col|colwidth=22em}} *[[Cubic honeycomb]] *[[Truncated cubic honeycomb]] *[[Bitruncated cubic honeycomb]] *[[Cantellated cubic honeycomb]] *[[Cantitruncated cubic honeycomb]] *[[Rectified cubic honeycomb]] *[[Runcitruncated cubic honeycomb]] *[[Omnitruncated cubic honeycomb]] *[[Tetrahedral-octahedral honeycomb]] *[[Truncated alternated cubic honeycomb]] *[[Cantitruncated alternated cubic honeycomb]] *[[Runcinated alternated cubic honeycomb]] *[[Quarter cubic honeycomb]] *[[Gyrated tetrahedral-octahedral honeycomb]] *[[Gyrated triangular prismatic honeycomb]] *[[Gyroelongated alternated cubic honeycomb]] *[[Gyroelongated triangular prismatic honeycomb]] *[[Elongated triangular prismatic honeycomb]] *[[Elongated alternated cubic honeycomb]] *[[Hexagonal prismatic honeycomb]] *[[Triangular prismatic honeycomb]] *[[Triangular-hexagonal prismatic honeycomb]] *[[Truncated hexagonal prismatic honeycomb]] *[[Truncated square prismatic honeycomb]] *[[Rhombitriangular-hexagonal prismatic honeycomb]] *[[Omnitruncated triangular-hexagonal prismatic honeycomb]] *[[Snub triangular-hexagonal prismatic honeycomb]] *[[Snub square prismatic honeycomb]] {{div col end}} ;Dual uniform honeycomb *[[Disphenoid tetrahedral honeycomb]] *[[Rhombic dodecahedral honeycomb]] ;Others *[[Trapezo-rhombic dodecahedral honeycomb]] *[[Weaire–Phelan structure]] ;[[Convex uniform honeycombs in hyperbolic space]] *[[Order-4 dodecahedral honeycomb]] *[[Order-5 cubic honeycomb]] *[[Order-5 dodecahedral honeycomb]] *[[Icosahedral honeycomb]] ===Other=== {{div col|colwidth=22em}} *[[Apeirogonal prism]] *[[Apeirohedron]] *[[Bicupola (geometry)|Bicupola]] *[[Cupola (geometry)|Cupola]] *[[Bifrustum]] *[[Boerdijk–Coxeter helix]] *[[Császár polyhedron]] *[[Flexible polyhedron]] *[[Gyroelongated square dipyramid]] *[[Heronian tetrahedron]] *[[Hexagonal bifrustum]] *[[Hexagonal truncated trapezohedron]] *[[Hill tetrahedron]] *[[Holyhedron]] *[[Infinite skew polyhedron]] *[[Jessen's icosahedron]] *[[Near-miss Johnson solid]] *[[Parallelepiped]] *[[Pentagonal bifrustum]] *[[Polytetrahedron]] *[[Pyritohedron]] *[[Rhombic enneacontahedron]] *[[Rhombic icosahedron]] *[[Rhombo-hexagonal dodecahedron]] *[[Rhombohedron]] *[[Scalenohedron]] *[[Schönhardt polyhedron]] *[[Square bifrustum]] *[[Square truncated trapezohedron]] *[[Szilassi polyhedron]] *[[Tetradecahedron]] *[[Tetradyakis hexahedron]] *[[Tetrated dodecahedron]] *[[Triangular bifrustum]] *[[Triaugmented triangular prism]] *[[Truncated rhombic dodecahedron]] *[[Truncated trapezohedron]] *[[Truncated triakis tetrahedron]] *[[Tridyakis icosahedron]] *[[Trigonal trapezohedron]] *[[Regular skew polyhedron]] *[[Waterman polyhedron]] *[[Wedge (geometry)|Wedge]] {{div col end}} ===Regular and uniform compound polyhedra=== ;[[Polyhedral compound]] and [[Uniform polyhedron compound]] {{div col|colwidth=22em}} *[[Compound of cube and octahedron]] *[[Compound of dodecahedron and icosahedron]] *[[Compound of eight octahedra with rotational freedom]] *[[Compound of eight triangular prisms]] *[[Compound of five cubes]] *[[Compound of five cuboctahedra]] *[[Compound of five cubohemioctahedra]] *[[Compound of five great cubicuboctahedra]] *[[Compound of five great dodecahedra]] *[[Compound of five great icosahedra]] *[[Compound of five great rhombihexahedra]] *[[Compound of five icosahedra]] *[[Compound of five octahedra]] *[[Compound of five octahemioctahedra]] *[[Compound of five small cubicuboctahedra]] *[[Compound of five small rhombicuboctahedra]] *[[Compound of five small rhombihexahedra]] *[[Compound of five small stellated dodecahedra]] *[[Compound of five stellated truncated cubes]] *[[Compound of five tetrahedra]] *[[Compound of five tetrahemihexahedra]] *[[Compound of five truncated cubes]] *[[Compound of five truncated tetrahedra]] *[[Compound of five uniform great rhombicuboctahedra]] *[[Compound of four hexagonal prisms]] *[[Compound of four octahedra]] *[[Compound of four octahedra with rotational freedom]] *[[Compound of four tetrahedra]] *[[Compound of four triangular prisms]] *[[Compound of great icosahedron and great stellated dodecahedron]] *[[Compound of six cubes with rotational freedom]] *[[Compound of six decagonal prisms]] *[[Compound of six decagrammic prisms]] *[[Compound of six pentagonal prisms]] *Compound of six pentagrammic crossed antiprisms *[[Compound of six pentagrammic prisms]] *[[Compound of six tetrahedra]] *[[Compound of six tetrahedra with rotational freedom]] *[[Compound of small stellated dodecahedron and great dodecahedron]] *[[Compound of ten hexagonal prisms]] *[[Compound of ten octahedra]] *[[Compound of ten tetrahedra]] *[[Compound of ten triangular prisms]] *[[Compound of ten truncated tetrahedra]] *[[Compound of three cubes]] *[[Compound of three tetrahedra]] *[[Compound of twelve pentagonal antiprisms with rotational freedom]] *[[Compound of twelve pentagonal prisms]] *[[Compound of twelve pentagrammic prisms]] *[[Compound of twelve tetrahedra with rotational freedom]] *[[Compound of twenty octahedra]] *[[Compound of twenty octahedra with rotational freedom]] *[[Compound of twenty tetrahemihexahedra]] *[[Compound of twenty triangular prisms]] *[[Compound of two great dodecahedra]] *[[Compound of two great icosahedra]] *[[Compound of two great inverted snub icosidodecahedra]] *[[Compound of two great retrosnub icosidodecahedra]] *[[Compound of two great snub icosidodecahedra]] *[[Compound of two icosahedra]] *[[Compound of two inverted snub dodecadodecahedra]] *[[Compound of two small stellated dodecahedra]] *[[Compound of two snub cubes]] *[[Compound of two snub dodecadodecahedra]] *[[Compound of two snub dodecahedra]] *[[Compound of two snub icosidodecadodecahedra]] *[[Compound of two truncated tetrahedra]] *[[Prismatic compound of antiprisms]] *[[Prismatic compound of antiprisms with rotational freedom]] *[[Prismatic compound of prisms]] *[[Prismatic compound of prisms with rotational freedom]] {{div col end}} *[[4-polytope]] **[[Hecatonicosachoron]] **[[Hexacosichoron]] **[[Hexadecachoron]] **[[Icositetrachoron]] **[[Pentachoron]] **[[Tesseract]] *[[Hypercone]] ;Convex [[regular 4-polytope]] *[[5-cell]], [[Tesseract]], [[16-cell]], [[24-cell]], [[120-cell]], [[600-cell]] ;[[Abstract regular polytope]] *[[11-cell]], [[57-cell]] ;[[regular 4-polytope|Schläfli–Hess 4-polytope]] (Regular star 4-polytope) *[[Icosahedral 120-cell]], [[Small stellated 120-cell]], [[Great 120-cell]], [[Grand 120-cell]], [[Great stellated 120-cell]], [[Grand stellated 120-cell]], [[Great grand 120-cell]], [[Great icosahedral 120-cell]], [[Grand 600-cell]], [[Great grand stellated 120-cell]] ;[[Uniform 4-polytope]] *[[Rectified 5-cell]], [[Truncated 5-cell]], [[Cantellated 5-cell]], [[Runcinated 5-cell]] *[[Rectified tesseract]], [[Truncated tesseract]], [[Cantellated tesseract]], [[Runcinated tesseract]] *[[Rectified 16-cell]], [[Truncated 16-cell]] *[[Rectified 24-cell]], [[Truncated 24-cell]], [[Cantellated 24-cell]], [[Runcinated 24-cell]], [[Snub 24-cell]] *[[Rectified 120-cell]], [[Truncated 120-cell]], [[Cantellated 120-cell]], [[Runcinated 120-cell]] *[[Rectified 600-cell]], [[Truncated 600-cell]], [[Cantellated 600-cell]] ;[[Prismatic uniform polychoron]] *[[Grand antiprism]] *[[Duoprism]] *[[Tetrahedral prism]], [[Truncated tetrahedral prism]] *[[Truncated cubic prism]], [[Truncated octahedral prism]], [[Cuboctahedral prism]], [[Rhombicuboctahedral prism]], [[Truncated cuboctahedral prism]], [[Snub cubic prism]] *[[Truncated dodecahedral prism]], [[Truncated icosahedral prism]], [[Icosidodecahedral prism]], [[Rhombicosidodecahedral prism]], [[Truncated icosidodecahedral prism]], [[Snub dodecahedral prism]] *[[Uniform antiprismatic prism]] ===Honeycombs=== *[[Tesseractic honeycomb]] *[[24-cell honeycomb]] *[[Snub 24-cell honeycomb]] *[[Rectified 24-cell honeycomb]] *[[Truncated 24-cell honeycomb]] *[[16-cell honeycomb]] *[[5-cell honeycomb]] *[[Omnitruncated 5-cell honeycomb]] *[[Truncated 5-cell honeycomb]] *[[Omnitruncated 5-simplex honeycomb]]
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