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
• 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

## Two dimensional (polygons)

Triangle
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
Triskaidecagon
Icosagon
Icosihenagon
Icosidigon
Icositrigon
Icositetragon
Icosipentagon
Icosihexagon
Icosiheptagon
Icosioctagon
Icosienneagon
Triacontagon
Tetracontagon
257-gon
hectogon
Chiliagon
Myriagon
65537-gon
Megagon
Apeirogon

### Tilings

Archimedean tiling

## Three dimensional (polyhedra)

Three-dimensional space

Tetrahedron
Pentahedron
Hexahedron
Heptahedron
Octahedron
Enneahedron
Decahedron
Dodecahedron

### Archimedean solids

Archimedean solid

Prism
Antiprism

Catalan solid

### Uniform star polyhedra

Uniform star polyhedron

### Uniform prismatic star polyhedra

Prismatic uniform polyhedron

Johnson solid

### Honeycombs

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

### Regular and uniform compound polyhedra

Polyhedral compound and Uniform polyhedron compound

## Four dimensions

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

## Five dimensions

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

## Six dimensions

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

## Seven dimensions

Seven-dimensional space, uniform 7-polytope

## Eight dimension

Eight-dimensional space, uniform 8-polytope

9-polytope

10-polytope

## Dimensional families

Regular polytope and List of regular polytopes
Uniform polytope
Honeycombs