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List of small polyhedra by vertex count

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In geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded by alternating faces and edges. The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices. Named polyhedra primarily come from the families of platonic solids, Archimedean solids, Catalan solids, and Johnson solids, as well as dihedral symmetry families including the pyramids, bipyramids, prisms, antiprisms, and trapezohedrons.

Polyhedra by vertex count

Notes: Polyhedra with different names that are topologically identical are listed together. Except in the cases of four and five vertices, the lists below are by no means exhaustive of all possible polyhedra with the given number of vertices, but rather just include particularly simple/common/well-known/named examples. The "Counting Polyhedra" link below gives the exact number of distinct polyhedra with n vertices for small values of n.

4	5	6	7	8	9	10	11	12	13	14	15
[[File:Tetrahedron.svg	100px]]Tetrahedrontriangular pyramid
[[File:Square pyramid.png	100px]]Square pyramid	[[File:Triangular dipyramid.png	100px]]
Triangular bipyramid
[[File:Pentagonal pyramid.png	100px]]Pentagonal pyramid	[[File:Octahedron.svg	100px]]Octahedron (regular)triangular antiprismsquare bipyramid	[[File:Triangular prism.png	100px]]Triangular prismwedge
[[File:Hexagonal pyramid.png	100px]]Hexagonal pyramid	[[File:Pentagonal dipyramid.png	100px]]Pentagonal bipyramid	[[File:Augmented triangular prism.png	100px]]Augmented triangular prism	[[File:Elongated triangular pyramid.png	100px]]Elongated triangular pyramid
Heptagonal pyramid	[[File:Hexagonale bipiramide.png	100px]]Hexagonal bipyramid	[[File:Hexahedron.png	100px]]HexahedronCubeSquare prismCuboidRhombohedronTrigonal trapezohedron	[[File:Square antiprism.png	100px]]Square antiprism	[[File:Triakistetrahedron.svg	100px]]Triakis tetrahedron	[[File:Elongated triangular dipyramid.png	100px]]Elongated triangular bipyramid
[[File:Gyrobifastigium.png	100px]]Gyrobifastigium	[[File:Snub disphenoid.png	100px]]Snub disphenoid	[[File:Biaugmented triangular prism.png	100px]]Biaugmented triangular prism
[[File:Triangular cupola.png	100px]]Triangular cupola	[[File:Triaugmented triangular prism.png	100px]]Triaugmented triangular prism	[[File:Elongated square pyramid.png	100px]]Elongated square pyramid	[[File:Gyroelongated square pyramid.png	100px]]Gyroelongated square pyramid	[[File:Tridiminished icosahedron.png	100px]]Tridiminished icosahedron
Octagonal pyramid	Heptagonal bipyramid
Nonagonal pyramid	[[File:Octagonal bipyramid.png	100px]]Octagonal bipyramid	[[File:Pentagonal prism.png	100px]]Pentagonal prism	[[File:Pentagonal antiprism.png	100px]]Pentagonal antiprism	[[File:Gyroelongated square dipyramid.png	100px]]Gyroelongated square bipyramid	[[File:Elongated square dipyramid.png	100px]]Elongated square bipyramid
[[File:Metabidiminished icosahedron.png	100px]]Metabidiminished icosahedron	[[File:Augmented tridiminished icosahedron.png	100px]]Augmented tridiminished icosahedron	[[File:Sphenocorona.png	100px]]Sphenocorona
Decagonal pyramid	Nonagonal bipyramid	[[File:Augmented pentagonal prism.png	100px]]Augmented pentagonal prism	[[File:Elongated pentagonal pyramid.png	100px]]Elongated pentagonal pyramid	[[File:Gyroelongated pentagonal pyramid.png	100px]]Gyroelongated pentagonal pyramid	[[File:Augmented sphenocorona.png	100px]]Augmented sphenocorona
[[File:Octadecahedron.png	100px]]Octadecahedron
[[File:Elongated pentagonal dipyramid.png	100px]]Elongated pentagonal bipyramid	[[File:Truncated tetrahedron.png	100px]]Truncated tetrahedron	[[File:Cuboctahedron.png	100px]]Cuboctahedron	[[File:Square cupola.png	100px]]Square cupola	[[File:Triangular orthobicupola.png	100px]]Triangular orthobicupola	[[File:Biaugmented pentagonal prism.png	100px]]Biaugmented pentagonal prism
Hendecagonal pyramid	[[File:Icosahedron.svg	100px]]Icosahedron	[[File:Decagonal bipyramid.png	100px]]Decagonal bipyramid	[[File:Hexagonal prism.png	100px]]Hexagonal prism	[[File:Hexagonal antiprism.png	100px]]Hexagonal antiprism	[[File:Sphenomegacorona.png	100px]]Sphenomegacorona
Dodecagonal pyramid	Hendecagonal bipyramid	[[File:Augmented hexagonal prism.png	100px]]Augmented hexagonal prism
Tridecagonal pyramid	Dodecagonal bipyramid	[[File:Elongated hexagonal dipyramid.png	100px]]Elongated hexagonal dipyramid	[[File:Prism 7.png	100px]]Heptagonal prism	[[File:Antiprism 7.png	100px]]Heptagonal antiprism	[[File:Rhombic dodecahedron.png	100px]]Rhombic dodecahedron
[[File:Parabiaugmented hexagonal prism.png	100px]]Parabiaugmented hexagonal prism	[[File:Metabiaugmented hexagonal prism.png	100px]]Metabiaugmented hexagonal prism	[[File:Hebesphenomegacorona.png	100px]]Hebesphenomegacorona	[[File:Bilunabirotunda.png	100px]]Bilunabirotunda	[[File:Tetrakishexahedron.jpg	100px]]Tetrakis hexahedron
Tetradecagonal pyramid	Tridecagonal bipyramid	Pentagonal cupola	Elongated triangular cupola
Gyroelongated triangular cupola
[[File:Octagonal prism.png	100px]]Octagonal prism	[[File:Octagonal antiprism.png	100px]]Octagonal antiprism	[[File:Triaugmented hexagonal prism.png	100px]]Triaugmented hexagonal prism	[[File:Augmented truncated tetrahedron.png	100px]]Augmented truncated tetrahedron	[[File:Square orthobicupola.png	100px]]Square orthobicupola	[[File:Square gyrobicupola.png	100px]]Square gyrobicupola
[[File:Disphenocingulum.png	100px]]Disphenocingulum	[[File:Snub square antiprism.png	100px]]Snub square antiprism
Hexadecagonal pyramid	Pentadecagonal bipyramid
[[File:Prism 9.png	100px]]Nonagonal prism	[[File:Enneagonal antiprism.png	100px]]Enneagonal antiprism	Gyroelongated triangular bicupola	Elongated triangular orthobicupola	Elongated triangular gyrobicupola	rhombocuboctohedron
[[File:Dodecahedron.svg	100px]]Dodecahedron	Pentagonal rotunda	Elongated square cupola	Gyroelongated square cupola	Pentagonal orthobicupola	Pentagonal gyrobicupola
[[File:Decagonal prism.png	100px]]Decagonal prism	[[File:Decagonal antiprism.png	100px]]Decagonal antiprism
Augmented dodecahedron
Parabiaugmented dodecahedron	Metabiaugmented dodecahedron
Triaugmented dodecahedron
[[File:Truncated hexahedron.png	100px]]Truncated cube	[[File:Truncated octahedron.png	100px]]Truncated octahedron	[[File:Small rhombicuboctahedron.png	100px]]Rhombicuboctahedron	[[File:Pseudorhombicuboctahedron.png	100px]]Elongated square gyrobicupola	[[File:Gyroelongated square bicupola.png	100px]]Gyroelongated square bicupola	[[File:Snubhexahedroncw.jpg	100px]]Snub cube

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