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
Polygon (2-polytope) Vertex the ridge or (n−2)-face of the polygon 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
Polychoron (4-polytope) 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
Polyteron (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 Golden triangle (mathematics) Scalene triangle Right triangle Oblique triangle Acute triangle Obtuse Triangle Quadrilateral Rectangle Square Unit square Oblong Golden rectangle Silver rectangle Ailles rectangle Rhombus Golden Rhombus Parallelogram Rhomboid Trapezoid Isosceles trapezoid Kite Lute of pythagoras Right Kite Antiparallelogram 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 Pentagram Hexagram Heptagram Octagram Enneagram Decagram Hendecagram Dodecagram Icositetragram
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 (polyhedra) 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 bipyramid, 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 bipyramid, Augmented pentagonal prism Dodecahedron Pentagonal antiprism, Decagonal prism, Pentagonal cupola, Snub disphenoid, Elongated square bipyramid, 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 bipyramid, Pentagonal bipyramid, Hexagonal bipyramid, Heptagonal bipyramid, Octagonal bipyramid, Decagonal bipyramid Trapezohedron Trigonal 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 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 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 Bifrusta Triangular bifrustum Square bifrustum Pentagonal bifrustum Hexagonal bifrustum Cupola Bifrustum Boerdijk–Coxeter helix Császár polyhedron Flexible polyhedron Goldberg polyhedron Heronian tetrahedron Hexagonal truncated trapezohedron Hill tetrahedron Holyhedron Infinite skew polyhedron Jessen's icosahedron Near-miss Johnson solid Tetrated dodecahedron Truncated triakis tetrahedron Parallelepiped Polytetrahedron Pyritohedron Rhombic enneacontahedron Rhombic icosahedron Rhombo-hexagonal dodecahedron Rhombohedron Scalenohedron Schönhardt polyhedron Square truncated trapezohedron Szilassi polyhedron Tetradecahedron Tetradyakis hexahedron Triaugmented triangular prism Truncated rhombic dodecahedron Truncated trapezohedron Tridyakis icosahedron 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 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
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, 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, 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, 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, Hexicated 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-demicube, Truncated 8-demicube, Cantellated 8-demicube, Runcinated 8-demicube, Stericated 8-demicube, Pentellated 8-demicube, Hexicated 8-demicube 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-orthoplex, Rectified 8-orthoplex, Truncated 8-orthoplex, Cantellated 8-orthoplex, Runcinated 8-orthoplex, Stericated 8-orthoplex, Pentellated 8-orthoplex, Hexicated 8-orthoplex, 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-simplex 9-demicube 9-cube 9-orthoplex
Hyperbolic honeycombs E9 honeycomb
Ten dimensions 10-polytope 10-simplex 10-demicube 10-cube 10-orthoplex
Dimensional families Regular 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 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
See also List of geometry topics