List of polygons, polyhedra and polytopes

Polygon (2-polytope)

Vertex

Edge the facet or (n−1)-face of the polygon

Polyhedron (3-polytope)

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

4-polytope

Vertex

Edge the peak or (n−3)-face of the 4-polytope

Face the ridge or (n−2)-face of the 4-polytope

Cell the facet or (n−1)-face of the 4-polytope

5-polytope

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

Point

Line segment

Vertex figure

Peak – (n−3)-face

Ridge – (n−2)-face

Facet – (n−1)-face

Two dimensional (polygons)

Triangle

Equilateral triangle

Isosceles triangle

Scalene triangle, Right triangle

Quadrilateral

Square

Quadrilateral

Rectangle

Rhombus

Parallelogram

Trapezoid

Isosceles trapezoid

Kite

Rhomboid

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Hendecagon

Dodecagon

Triskaidecagon

Tetradecagon

Pentadecagon

Hexadecagon

Heptadecagon

Octadecagon

Enneadecagon

Icosagon

Icositetragon

Triacontagon

Tetracontagon

257-gon

Chiliagon

Myriagon

65537-gon

Megagon

Apeirogon

Star polygons

Pentagram

Hexagram

Heptagram

Octagram

Enneagram

Decagram

Hendecagram

Dodecagram

Families

Concave polygon

Cyclic polygon

Regular polygon

Polyform

Gnomon

Golygon

Tilings

List of uniform tilings Uniform 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 tiling

Three dimensional

Three-dimensional space

Regular

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

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

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

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

Bipyramid

Triangular dipyramid, Pentagonal dipyramid, Hexagonal bipyramid, Octagonal bipyramid, Decagonal bipyramid

Trapezohedron

Uniform star polyhedra

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

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

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

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

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

Apeirogonal prism

Apeirohedron

Bicupola

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

Regular and uniform compound polyhedra

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 antiprisms

Compound of six pentagonal prisms

Compound of six pentagrammic antiprisms

Compound of six pentagrammic crossed antiprisms

Compound of six pentagrammic prisms

Compound of six square antiprisms

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 square antiprisms

Compound of three tetrahedra

Compound of twelve pentagonal antiprisms with rotational freedom

Compound of twelve pentagonal prisms

Compound of twelve pentagrammic antiprisms

Compound of twelve pentagrammic crossed antiprisms with rotational freedom

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

Four dimensions

Four-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

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

Five dimensions

Five-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, 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

5-cubic honeycomb

5-simplex honeycomb

Truncated 5-simplex honeycomb

5-demicubic honeycomb

Six dimensions

Six-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, 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

6-cubic honeycomb

6-simplex honeycomb

6-demicubic honeycomb

2₂₂ honeycomb

Seven dimensions

Seven-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

7-cubic honeycomb

7-demicubic honeycomb

3₃₁ honeycomb, 1₃₃ honeycomb

Eight dimension

Eight-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

8-cubic honeycomb

8-demicubic honeycomb

5₂₁ honeycomb, 2₅₁ honeycomb, 1₅₂ honeycomb

Nine dimensions

9-polytope

9-cube

9-demicube

9-orthoplex

9-simplex

Hyperbolic honeycombs

E₉ honeycomb

Ten dimensions

10-polytope

10-cube

10-demicube

10-orthoplex

10-simplex

Dimensional families

Regular polytope and List of regular polytopes

Simplex

Hypercube

Cross-polytope

Uniform polytope

Demihypercube

Uniform 1_k2 polytope

Uniform 2_k1 polytope

Uniform k₂₁ polytope

Honeycombs

Hypercubic honeycomb

Alternated hypercubic honeycomb

Geometric operators

Rectification (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 notation