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List of polygons, polyhedra and polytopes

May 07, 2024

A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.

Polytope elements edit

Polygon (2-polytope) edit

  • Vertex the ridge or (n−2)-face of the polygon
  • Edge the facet or (n−1)-face of the polygon

Polyhedron (3-polytope) edit

  • Vertex the peak or (n−3)-face of the polyhedron
  • Edge the ridge or (n−2)-face of the polyhedron
  • Face the facet or (n−1)-face of the polyhedron

Polychoron (4-polytope) edit

  • Vertex the (n−4)-face of the polychoron
  • Edge the peak or (n−3)-face of the polychoron
  • Face the ridge or (n−2)-face of the polychoron
  • Cell the facet or (n−1)-face of the polychoron

5-polytope edit

  • Vertex the (n−5)-face of the 5-polytope
  • Edge the (n−4)-face of the 5-polytope
  • Face the peak or (n−3)-face of the 5-polytope
  • Cell the ridge or (n−2)-face of the 5-polytope
  • Hypercell or Teron the facet or (n−1)-face of the 5-polytope

Other edit

Two dimensional (polygons) edit

Triangle
Quadrilateral

Star polygons edit

Families edit

Tilings edit

List of uniform tilings

Uniform tilings in hyperbolic plane

Archimedean tiling

Three dimensional (polyhedra) edit

Three-dimensional space

Regular edit

Regular polyhedron

Tetrahedron
Pentahedron
Hexahedron
Heptahedron
Octahedron
Enneahedron
Decahedron
Dodecahedron

Archimedean solids edit

Archimedean solid

Prisms and antiprisms edit

Prism
Antiprism

Catalan solids edit

Catalan solid

Bipyramids and Trapezohedron edit

Uniform star polyhedra edit

Uniform star polyhedron

Uniform prismatic star polyhedra edit

Prismatic uniform polyhedron

Johnson solids edit

Johnson solid
  1. Augmented dodecahedron
  2. Augmented hexagonal prism
  3. Augmented pentagonal prism
  4. Augmented sphenocorona
  5. Augmented triangular prism
  6. Augmented tridiminished icosahedron
  7. Augmented truncated cube
  8. Augmented truncated dodecahedron
  9. Augmented truncated tetrahedron
  10. Biaugmented pentagonal prism
  11. Biaugmented triangular prism
  12. Biaugmented truncated cube
  13. Bigyrate diminished rhombicosidodecahedron
  14. Bilunabirotunda
  15. Diminished rhombicosidodecahedron
  16. Disphenocingulum
  17. Elongated pentagonal bipyramid
  18. Elongated pentagonal cupola
  19. Elongated pentagonal gyrobicupola
  20. Elongated pentagonal gyrobirotunda
  21. Elongated pentagonal gyrocupolarotunda
  22. Elongated pentagonal orthobicupola
  23. Elongated pentagonal orthobirotunda
  24. Elongated pentagonal orthocupolarotunda
  25. Elongated pentagonal pyramid
  26. Elongated pentagonal rotunda
  27. Elongated square bipyramid
  28. Elongated square cupola
  29. Elongated square gyrobicupola
  30. Elongated square pyramid
  31. Elongated triangular bipyramid
  32. Elongated triangular cupola
  33. Elongated triangular gyrobicupola
  34. Elongated triangular orthobicupola
  35. Elongated triangular pyramid
  36. Gyrate bidiminished rhombicosidodecahedron
  37. Gyrate rhombicosidodecahedron
  38. Gyrobifastigium
  39. Gyroelongated pentagonal bicupola
  40. Gyroelongated pentagonal birotunda
  41. Gyroelongated pentagonal cupola
  42. Gyroelongated pentagonal cupolarotunda
  43. Gyroelongated pentagonal pyramid
  44. Gyroelongated pentagonal rotunda
  45. Gyroelongated square bicupola
  46. Gyroelongated square bipyramid
  47. Gyroelongated square cupola
  48. Gyroelongated square pyramid
  49. Gyroelongated triangular bicupola
  50. Gyroelongated triangular cupola
  51. Hebesphenomegacorona
  52. Metabiaugmented dodecahedron
  53. Metabiaugmented hexagonal prism
  54. Metabiaugmented truncated dodecahedron
  55. Metabidiminished icosahedron
  56. Metabidiminished rhombicosidodecahedron
  57. Metabigyrate rhombicosidodecahedron
  58. Metagyrate diminished rhombicosidodecahedron
  59. Parabiaugmented dodecahedron
  60. Parabiaugmented hexagonal prism
  61. Parabiaugmented truncated dodecahedron
  62. Parabidiminished rhombicosidodecahedron
  63. Parabigyrate rhombicosidodecahedron
  64. Paragyrate diminished rhombicosidodecahedron
  65. Pentagonal bipyramid
  66. Pentagonal cupola
  67. Pentagonal gyrobicupola
  68. Pentagonal gyrocupolarotunda
  69. Pentagonal orthobicupola
  70. Pentagonal orthobirotunda
  71. Pentagonal orthocupolarotunda
  72. Pentagonal pyramid
  73. Pentagonal rotunda
  74. Snub disphenoid
  75. Snub square antiprism
  76. Sphenocorona
  77. Sphenomegacorona
  78. Square cupola
  79. Square gyrobicupola
  80. Square orthobicupola
  81. Square pyramid
  82. Triangular bipyramid
  83. Triangular cupola
  84. Triangular hebesphenorotunda
  85. Triangular orthobicupola
  86. Triaugmented dodecahedron
  87. Triaugmented hexagonal prism
  88. Triaugmented triangular prism
  89. Triaugmented truncated dodecahedron
  90. Tridiminished icosahedron
  91. Tridiminished rhombicosidodecahedron
  92. Trigyrate rhombicosidodecahedron

Dual uniform star polyhedra edit

Honeycombs edit

Convex uniform honeycomb
Dual uniform honeycomb
Others
Convex uniform honeycombs in hyperbolic space

Other edit

Regular and uniform compound polyhedra edit

Polyhedral compound and Uniform polyhedron compound

Four dimensions edit

Four-dimensional space

4-polytope – general term for a four dimensional polytope

Regular 4-polytope
Abstract regular polytope
Regular star 4-polytope
Uniform 4-polytope
Prismatic uniform 4-polytope
Uniform antiprismatic prism

Honeycombs edit

Five dimensions edit

Five-dimensional space, 5-polytope and uniform 5-polytope
Prismatic uniform 5-polytope
  • 5-cell prism, Rectified 5-cell prism, Truncated 5-cell prism, Cantellated 5-cell prism, Runcinated 5-cell prism, Bitruncated 5-cell prism, Cantitruncated 5-cell prism, Runcitruncated 5-cell prism, Omnitruncated 5-cell prism
  • Tesseractic prism, Rectified tesseractic prism, Truncated tesseractic prism, Cantellated tesseractic prism, Runcinated tesseractic prism, Bitruncated tesseractic prism, Cantitruncated tesseractic prism, Runcitruncated tesseractic prism, Omnitruncated tesseractic prism
  • 16-cell prism, Truncated 16-cell prism, Runcitruncated 16-cell prism
  • 24-cell prism, rectified 24-cell prism, truncated 24-cell prism, cantellated 24-cell prism, runcinated 24-cell prism, bitruncated 24-cell prism, cantitruncated 24-cell prism, runcitruncated 24-cell prism, omnitruncated 24-cell prism, snub 24-cell prism
  • 120-cell prism, Rectified 120-cell prism, Truncated 120-cell prism, Cantellated 120-cell prism, Runcinated 120-cell prism, Bitruncated 120-cell prism, Cantitruncated 120-cell prism, Runcitruncated 120-cell prism, Omnitruncated 120-cell prism
  • 600-cell prism, Rectified 600-cell prism, Truncated 600-cell prism, Cantellated 600-cell prism, Cantitruncated 600-cell prism, Runcitruncated 600-cell prism
  • Grand antiprism prism

Honeycombs edit

Six dimensions edit

Six-dimensional space, 6-polytope and uniform 6-polytope

Honeycombs edit

Seven dimensions edit

Seven-dimensional space, uniform 7-polytope

Honeycombs edit

Eight dimension edit

Eight-dimensional space, uniform 8-polytope

Honeycombs edit

Nine dimensions edit

9-polytope

Hyperbolic honeycombs edit

Ten dimensions edit

10-polytope

Dimensional families edit

Regular polytope and List of regular polytopes
Uniform polytope
Honeycombs

Geometric operators edit

See also edit

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron
Uniform polychoron Pentachoron 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell
Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221
Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321
Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421
Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds

May 07, 2024
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A polytope is a geometric object with flat sides which exists in any general number of dimensions The following list of polygons polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples Contents 1 Polytope elements 1 1 Polygon 2 polytope 1 2 Polyhedron 3 polytope 1 3 Polychoron 4 polytope 1 4 5 polytope 1 5 Other 2 Two dimensional polygons 2 1 Star polygons 2 2 Families 2 3 Tilings 3 Three dimensional polyhedra 3 1 Regular 3 2 Archimedean solids 3 3 Prisms and antiprisms 3 4 Catalan solids 3 5 Bipyramids and Trapezohedron 3 6 Uniform star polyhedra 3 7 Uniform prismatic star polyhedra 3 8 Johnson solids 3 9 Dual uniform star polyhedra 3 10 Honeycombs 3 11 Other 3 12 Regular and uniform compound polyhedra 4 Four dimensions 4 1 Honeycombs 5 Five dimensions 5 1 Honeycombs 6 Six dimensions 6 1 Honeycombs 7 Seven dimensions 7 1 Honeycombs 8 Eight dimension 8 1 Honeycombs 9 Nine dimensions 9 1 Hyperbolic honeycombs 10 Ten dimensions 11 Dimensional families 12 Geometric operators 13 See alsoPolytope elements editPolygon 2 polytope edit Vertex the ridge or n 2 face of the polygon Edge the facet or n 1 face of the polygon Polyhedron 3 polytope edit Vertex the peak or n 3 face of the polyhedron Edge the ridge or n 2 face of the polyhedron Face the facet or n 1 face of the polyhedron Polychoron 4 polytope edit Vertex the n 4 face of the polychoron Edge the peak or n 3 face of the polychoron Face the ridge or n 2 face of the polychoron Cell the facet or n 1 face of the polychoron 5 polytope edit Vertex the n 5 face of the 5 polytope Edge the n 4 face of the 5 polytope Face the peak or n 3 face of the 5 polytope Cell the ridge or n 2 face of the 5 polytope Hypercell or Teron the facet or n 1 face of the 5 polytope Other edit Point Line segment Vertex figure Peak n 3 face Ridge n 2 face Facet n 1 faceTwo dimensional polygons editTriangle Equilateral triangle Isosceles triangle Scalene triangle Right triangle Oblique triangle Acute triangle Obtuse Triangle Quadrilateral Rectangle Square Rhombus Parallelogram Trapezoid Isosceles trapezoid Kite Rhomboid Pentagon Hexagon Heptagon Octagon Nonagon Decagon Hendecagon Dodecagon Triskaidecagon Tetradecagon Pentadecagon Hexadecagon Heptadecagon Octadecagon Enneadecagon Icosagon Icosihenagon Icosidigon Icositrigon Icositetragon Icosipentagon Icosihexagon Icosiheptagon Icosioctagon Icosienneagon Triacontagon Tetracontagon Pentacontagon Hexacontagon Heptacontagon Octacontagon Enneacontagon Hectogon 257 gon Chiliagon Myriagon 65537 gon Megagon Gigagon Teragon Apeirogon Star polygons edit Pentagram Hexagram Heptagram Octagram Enneagram Decagram Hendecagram Dodecagram Icositetragram Families edit Concave polygon Cyclic polygon Regular polygon Polyform Gnomon Golygon Tilings edit List of uniform tilingsUniform tilings in hyperbolic plane 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 tilingThree dimensional polyhedra editThree dimensional space Regular edit Regular polyhedron Platonic solid Tetrahedron Cube Octahedron Dodecahedron Icosahedron Regular spherical polyhedron Dihedron Hosohedron Kepler Poinsot polyhedron Regular star polyhedra Small stellated dodecahedron Great stellated dodecahedron Great icosahedron Great dodecahedron Abstract regular polyhedra Projective polyhedron Hemicube geometry hemi octahedron hemi dodecahedron hemi icosahedron Tetrahedron Disphenoid Pentahedron Square pyramid Triangular prism Hexahedron Parallelepiped Cuboid Rhombohedron Trigonal trapezohedron Cube Pentagonal pyramid Triangular dipyramid quadrilateral frustum Heptahedron hexagonal pyramid pentagonal prism tetrahemihexahedron Octahedron Hexagonal prism Truncated tetrahedron Tetragonal trapezohedron Enneahedron Octagonal pyramid Heptagonal prism Decahedron Octagonal prism Square antiprism Square cupola Pentagonal dipyramid Augmented pentagonal prism Dodecahedron Pentagonal antiprism Decagonal prism Pentagonal cupola Snub disphenoid Elongated square dipyramid Metabidiminished icosahedron Hexagonal bipyramid Hexagonal trapezohedron Triakis tetrahedron Rhombic dodecahedron Hendecagonal pyramid Trapezo rhombic dodecahedron Rhombo hexagonal dodecahedron Archimedean solids edit Archimedean solid Truncated tetrahedron Cuboctahedron Truncated cube Truncated octahedron Rhombicuboctahedron Truncated cuboctahedron Snub cube Icosidodecahedron Truncated dodecahedron Truncated icosahedron Rhombicosidodecahedron Truncated icosidodecahedron Snub dodecahedron Prisms and antiprisms edit Prism Triangular prism Pentagonal prism Hexagonal prism Heptagonal prism Octagonal prism Enneagonal prism Decagonal prism Hendecagonal prism Dodecagonal prism Antiprism Square antiprism Pentagonal antiprism Hexagonal antiprism Heptagonal antiprism Octagonal antiprism Enneagonal antiprism Decagonal antiprism Dodecagonal antiprism Catalan solids edit 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 Bipyramids and Trapezohedron edit Bipyramid Triangular dipyramid Pentagonal dipyramid Hexagonal bipyramid Octagonal bipyramid Decagonal bipyramid Trapezohedron Uniform star polyhedra edit Uniform star polyhedron 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 Uniform prismatic star polyhedra edit Prismatic uniform polyhedron Pentagrammic prism Pentagrammic antiprism Pentagrammic crossed antiprism Heptagrammic antiprism 7 2 Heptagrammic antiprism 7 3 Enneagrammic antiprism 9 2 Enneagrammic antiprism 9 4 Enneagrammic crossed antiprism Enneagrammic prism 9 2 Enneagrammic prism 9 4 Decagrammic prism Decagrammic antiprism Johnson solids edit Johnson solid 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 Dual uniform star polyhedra edit 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 Honeycombs edit Convex uniform honeycomb 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 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 edit Apeirogonal prism Apeirohedron Bicupola Cupola Bifrustum Boerdijk Coxeter helix Csaszar polyhedron Flexible polyhedron Gyroelongated square bipyramid 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 Schonhardt 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 Regular and uniform compound polyhedra edit Polyhedral compound and Uniform polyhedron compound 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 freedomFour dimensions editFour dimensional space 4 polytope general term for a four dimensional polytope Regular 4 polytope 5 cell Tesseract 16 cell 24 cell 120 cell 600 cell Abstract regular polytope 11 cell 57 cell 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 4 polytope 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 Triangular antiprismatic prism Square antiprismatic prism Pentagonal antiprismatic prism Hexagonal antiprismatic prism Heptagonal antiprismatic prism Octagonal antiprismatic prism Enneagonal antiprismatic prism Decagonal antiprismatic prism Pentagrammic antiprismatic prism Hexagrammic antiprismatic prism Heptagrammic antiprismatic prism Octagrammic antiprismatic prism Enneagrammic antiprismatic prism Decagrammic antiprismatic prism Pentagrammic crossed antiprismatic prism Hexagrammic crossed antiprismatic prism Heptagrammic crossed antiprismatic prism Octagrammic crossed antiprismatic prism Enneagrammic crossed antiprismatic prism Decagrammic crossed antiprismatic prism Honeycombs edit 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 honeycombFive dimensions editFive dimensional space 5 polytope and uniform 5 polytope 5 simplex Rectified 5 simplex Truncated 5 simplex Cantellated 5 simplex Runcinated 5 simplex Stericated 5 simplex 5 demicube Truncated 5 demicube Cantellated 5 demicube Runcinated 5 demicube 5 cube Rectified 5 cube Truncated 5 cube Cantellated 5 cube Runcinated 5 cube Stericated 5 cube 5 orthoplex Rectified 5 orthoplex Truncated 5 orthoplex Cantellated 5 orthoplex Runcinated 5 orthoplex Prismatic uniform 5 polytope 5 cell prism Rectified 5 cell prism Truncated 5 cell prism Cantellated 5 cell prism Runcinated 5 cell prism Bitruncated 5 cell prism Cantitruncated 5 cell prism Runcitruncated 5 cell prism Omnitruncated 5 cell prism Tesseractic prism Rectified tesseractic prism Truncated tesseractic prism Cantellated tesseractic prism Runcinated tesseractic prism Bitruncated tesseractic prism Cantitruncated tesseractic prism Runcitruncated tesseractic prism Omnitruncated tesseractic prism 16 cell prism Truncated 16 cell prism Runcitruncated 16 cell prism 24 cell prism rectified 24 cell prism truncated 24 cell prism cantellated 24 cell prism runcinated 24 cell prism bitruncated 24 cell prism cantitruncated 24 cell prism runcitruncated 24 cell prism omnitruncated 24 cell prism snub 24 cell prism 120 cell prism Rectified 120 cell prism Truncated 120 cell prism Cantellated 120 cell prism Runcinated 120 cell prism Bitruncated 120 cell prism Cantitruncated 120 cell prism Runcitruncated 120 cell prism Omnitruncated 120 cell prism 600 cell prism Rectified 600 cell prism Truncated 600 cell prism Cantellated 600 cell prism Cantitruncated 600 cell prism Runcitruncated 600 cell prism Grand antiprism prism Honeycombs edit 5 cubic honeycomb 5 simplex honeycomb Truncated 5 simplex honeycomb 5 demicubic honeycombSix dimensions editSix dimensional space 6 polytope and uniform 6 polytope 6 simplex Rectified 6 simplex Truncated 6 simplex Cantellated 6 simplex Runcinated 6 simplex Stericated 6 simplex Pentellated 6 simplex 6 demicube Truncated 6 demicube Cantellated 6 demicube Runcinated 6 demicube Stericated 6 demicube 6 cube Rectified 6 cube Truncated 6 cube Cantellated 6 cube Runcinated 6 cube Stericated 6 cube Pentellated 6 cube 6 orthoplex Rectified 6 orthoplex Truncated 6 orthoplex Cantellated 6 orthoplex Runcinated 6 orthoplex Stericated 6 orthoplex 122 polytope 221 polytope Honeycombs edit 6 cubic honeycomb 6 simplex honeycomb 6 demicubic honeycomb 222 honeycombSeven dimensions editSeven dimensional space uniform 7 polytope 7 simplex Rectified 7 simplex Truncated 7 simplex Cantellated 7 simplex Runcinated 7 simplex Stericated 7 simplex Pentellated 7 simplex Hexicated 7 simplex 7 demicube Truncated 7 demicube Cantellated 7 demicube Runcinated 7 demicube Stericated 7 demicube Pentellated 7 demicube 7 cube Rectified 7 cube 7 cube Truncated 7 cube Cantellated 7 cube Runcinated 7 cube Stericated 7 cube Pentellated 7 cube Hexicated 7 cube 7 orthoplex Rectified 7 orthoplex Truncated 7 orthoplex Cantellated 7 orthoplex Runcinated 7 orthoplex Stericated 7 orthoplex Pentellated 7 orthoplex 132 polytope 231 polytope 321 polytope Honeycombs edit 7 cubic honeycomb 7 demicubic honeycomb 331 honeycomb 133 honeycombEight dimension editEight dimensional space uniform 8 polytope 8 simplex Rectified 8 simplex Truncated 8 simplex Cantellated 8 simplex Runcinated 8 simplex Stericated 8 simplex Pentellated 8 simplex Hexicated 8 simplex Heptellated 8 simplex 8 orthoplex Rectified 8 orthoplex Truncated 8 orthoplex Cantellated 8 orthoplex Runcinated 8 orthoplex Stericated 8 orthoplex Pentellated 8 orthoplex Hexicated 8 orthoplex 8 cube Rectified 8 cube Truncated 8 cube Cantellated 8 cube Runcinated 8 cube Stericated 8 cube Pentellated 8 cube Hexicated 8 cube Heptellated 8 cube 8 demicube Truncated 8 demicube Cantellated 8 demicube Runcinated 8 demicube Stericated 8 demicube Pentellated 8 demicube Hexicated 8 demicube 142 polytope 241 polytope 421 polytope Truncated 421 polytope Truncated 241 polytope Truncated 142 polytope Cantellated 421 polytope Cantellated 241 polytope Runcinated 421 polytope Honeycombs edit 8 cubic honeycomb 8 demicubic honeycomb 521 honeycomb 251 honeycomb 152 honeycombNine dimensions edit9 polytope 9 cube 9 demicube 9 orthoplex 9 simplex Hyperbolic honeycombs edit E9 honeycombTen dimensions edit10 polytope 10 cube 10 demicube 10 orthoplex 10 simplexDimensional families editRegular polytope and List of regular polytopes Simplex Hypercube Cross polytope Uniform polytope Demihypercube Uniform 1k2 polytope Uniform 2k1 polytope Uniform k21 polytope Honeycombs Hypercubic honeycomb Alternated hypercubic honeycombGeometric operators editRectification geometry Truncation geometry Bitruncation Cantellation Runcination Sterication Omnitruncation Expansion geometry Snub geometry Alternation geometry Dual polyhedron Gyration geometry Elongation geometry Augmentation geometry Diminishment geometry Greatening geometry Aggrandizement geometry Stellation Kleetope Conway polyhedron notationSee also editList of geometry topics vteFundamental convex regular and uniform polytopes in dimensions 2 10 Family An Bn I2 p Dn E6 E7 E8 F4 G2 Hn Regular polygon Triangle Square p gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron Cube Demicube Dodecahedron Icosahedron Uniform polychoron Pentachoron 16 cell Tesseract Demitesseract 24 cell 120 cell 600 cell Uniform 5 polytope 5 simplex 5 orthoplex 5 cube 5 demicube Uniform 6 polytope 6 simplex 6 orthoplex 6 cube 6 demicube 122 221 Uniform 7 polytope 7 simplex 7 orthoplex 7 cube 7 demicube 132 231 321 Uniform 8 polytope 8 simplex 8 orthoplex 8 cube 8 demicube 142 241 421 Uniform 9 polytope 9 simplex 9 orthoplex 9 cube 9 demicube Uniform 10 polytope 10 simplex 10 orthoplex 10 cube 10 demicube Uniform n polytope n simplex n orthoplex n cube n demicube 1k2 2k1 k21 n pentagonal polytope Topics Polytope families Regular polytope List of regular polytopes and compounds Retrieved from https en wikipedia org w index php title List of polygons polyhedra and polytopes amp oldid 1178194512, wikipedia, wiki, book, books, library,

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