# List of polygons, polyhedra and polytopes

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

## Polytope elements[edit]

### Polygon (2-polytope)[edit]

### 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

### 4-polytope[edit]

- 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[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)-face*

## Two dimensional (polygons)[edit]

- 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
- 257-gon
- Chiliagon
- Myriagon
- 65537-gon
- Megagon
- Apeirogon

### Star polygons[edit]

### Families[edit]

### Tilings[edit]

List of uniform tilings Uniform tilings in hyperbolic plane

- 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)[edit]

### Regular[edit]

- Platonic solid:
- Regular spherical polyhedron
- Kepler–Poinsot polyhedron (Regular star polyhedra)
- Abstract regular polyhedra (Projective polyhedron)

- Parallelepiped, Cuboid, Rhombohedron, Trigonal trapezohedron, Cube, Pentagonal pyramid, Triangular dipyramid, quadrilateral frustum

- 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]

- 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]

- Triangular prism, Pentagonal prism, Hexagonal prism, Heptagonal prism, Octagonal prism, Enneagonal prism, Decagonal prism, Hendecagonal prism, Dodecagonal prism

- Square antiprism, Pentagonal antiprism, Hexagonal antiprism, Heptagonal antiprism, Octagonal antiprism, Enneagonal antiprism, Decagonal antiprism, Dodecagonal antiprism

### Catalan solids[edit]

- 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]

### Uniform star polyhedra[edit]

- 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]

- 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]

- 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]

- 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

- Others

- 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
- 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[edit]

- 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[edit]

4-polytope – general term for a four dimensional 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

- 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

- 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

- 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 honeycomb

## Five dimensions[edit]

- 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

- 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]

- 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
- 1
_{22}polytope, 2_{21}polytope

### Honeycombs[edit]

## Seven dimensions[edit]

- 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
- 1
_{32}polytope, 2_{31}polytope, 3_{21}polytope

### Honeycombs[edit]

## Eight dimension[edit]

- 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
- 1
_{42}polytope, 2_{41}polytope, 4_{21}polytope, Truncated 4_{21}polytope, Truncated 2_{41}polytope, Truncated 1_{42}polytope, Cantellated 4_{21}polytope, Cantellated 2_{41}polytope, Runcinated 4_{21}polytope

### Honeycombs[edit]

## Nine dimensions[edit]

### Hyperbolic honeycombs[edit]

## Ten dimensions[edit]

## Dimensional families[edit]

- Honeycombs

## Geometric operators[edit]

- 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