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# List of polygons, polyhedra and polytopes

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 Title: List of polygons, polyhedra and polytopes Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### 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 1
• Polygon (2-polytope) 1.1
• Polyhedron (3-polytope) 1.2
• 4-polytope 1.3
• 5-polytope 1.4
• Other 1.5
• Two dimensional 2
• Families 2.1
• Tilings 2.2
• Other 2.3
• Three dimensional 3
• Regular 3.1
• Archimedean solids 3.2
• Prisms and antiprisms 3.3
• Catalan solids 3.4
• Bipyramids and Trapezohedron 3.5
• Uniform star polyhedra 3.6
• Uniform prismatic star polyhedra 3.7
• Johnson solids 3.8
• Dual uniform star polyhedra 3.9
• Honeycombs 3.10
• Other 3.11
• Regular and uniform compound polyhedra 3.12
• Four dimensions 4
• Honeycombs 4.1
• Five dimensions 5
• Honeycombs 5.1
• Six dimensions 6
• Honeycombs 6.1
• Seven dimensions 7
• Honeycombs 7.1
• Eight dimension 8
• Honeycombs 8.1
• Nine dimensions 9
• Hyperbolic honeycombs 9.1
• Ten dimensions 10
• Dimensional families 11
• Geometric operators 12

## 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

Triangle
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
Triskaidecagon
Icosagon
Icositetragon
Triacontagon
Tetracontagon
257-gon
Chiliagon
Myriagon
65537-gon
Megagon
Gnomon
Golygon
Star polygons

### Tilings

Archimedean tiling

## Three dimensional

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

## 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