List Of Convex Regular-Faced Polyhedra

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This is a list of convex, regular-faced polyhedra. Since there are an infinite number of prisms and antiprisms, only a few have been listed.

Name Platonic? Archimedean? Prism? Antiprism? Pyramid? Dipyramid? Deltahedron? Faces (3) Faces (4) Faces (5) Faces (6) Faces (8) Faces (10) Faces (12) Faces (n) Edges Vertices
Tetrahedron Yes No No No Yes No Yes 4 0 0 0 0 0 0 - 6 4
Cube Yes No Yes No No No No 0 6 0 0 0 0 0 - 12 8
Octahedron Yes No No Yes No Yes Yes 8 0 0 0 0 0 0 - 12 6
Dodecahedron Yes No No No No No No 0 0 12 0 0 0 0 - 30 20
Icosahedron Yes No No No No No Yes 20 0 0 0 0 0 0 - 30 12
Truncated tetrahedron No Yes No No No No No 4 0 0 4 0 0 0 - 18 12
Cuboctahedron No Yes No No No No No 8 6 0 0 0 0 0 - 24 12
Truncated cube No Yes No No No No No 8 0 0 0 6 0 0 - 36 24
Truncated octahedron No Yes No No No No No 0 6 0 8 0 0 0 - 36 24
Rhombicuboctahedron No Yes No No No No No 8 18 0 0 0 0 0 - 48 24
Great rhombicuboctahedron No Yes No No No No No 0 12 0 8 6 0 0 - 72 48
Snub cube No Yes No No No No No 32 6 0 0 0 0 0 - 60 24
Icosidodecahedron No Yes No No No No No 20 0 12 0 0 0 0 - 60 30
Truncated dodecahedron No Yes No No No No No 20 0 0 0 0 12 0 - 90 60
Truncated icosahedron No Yes No No No No No 0 0 12 20 0 0 0 - 90 60
Rhombicosidodecahedron No Yes No No No No No 20 30 12 0 0 0 0 - 120 60
Great rhombicosidodecahedron No Yes No No No No No 0 30 0 20 0 12 0 - 180 120
Snub dodecahedron No Yes No No No No No 80 0 12 0 0 0 0 - 150 60
Triangular prism No Yes Yes No No No No 2 3 0 0 0 0 0 - 9 6
Pentagonal prism No Yes Yes No No No No 0 5 2 0 0 0 0 - 15 10
Octagonal prism No Yes Yes No No No No 0 8 0 0 2 0 0 - 24 16
n-prism No Yes Yes No No No No - n - - - - - 2 3n 2n
Square antiprism No Yes No Yes No No No 8 2 0 0 0 0 0 - 16 8
Pentagonal antiprism No Yes No Yes No No No 10 0 2 0 0 0 0 - 20 10
n-antiprism No Yes No Yes No No No 2n - - - - - - 2 4n 2n
Square pyramid No No No No Yes No No 4 1 0 0 0 0 0 - 8 5
Pentagonal pyramid No No No No Yes No No 5 0 1 0 0 0 0 - 10 6
Triangular cupola No No No No No No No 4 3 0 1 0 0 0 - 15 9
Square cupola No No No No No No No 4 5 0 0 1 0 0 - 20 12
Pentagonal cupola No No No No No No No 5 5 1 0 0 1 0 - 25 15
Pentagonal rotunda No No No No No No No 10 0 6 0 0 1 0 - 35 20
Gyroelongated pentagonal pyramid No No No No No No No
Triangular dipyramid No No No No No Yes Yes
Pentagonal dipyramid No No No No No Yes Yes
Gyroelongated square dipyramid No No No No No No Yes
Elongated square cupola No No No No No No No
Elongated square gyrobicupola No No No No No No No 8 18 0 0 0 0 0 - 48 24
Triaugmented triangular prism No No No No No No Yes
Metabidiminished icosahedron No No No No No No No
Tridiminished icosahedron No No No No No No No
Diminished rhombicosidodecahedron No No No No No No No
Parabidiminished rhombicosidodecahedron No No No No No No No
Metabidiminished rhombicosidodecahedron No No No No No No No
Tridiminished rhombicosidodecahedron No No No No No No No
Snub disphenoid No No No No No No Yes
Snub square antiprism No No No No No No No
Sphenocorona No No No No No No No
Sphenomegacorona No No No No No No No
Hebesphenomegacorona No No No No No No No
Disphenocingulum No No No No No No No
Bilunabirotunda No No No No No No No
Triangular hebesphenorotunda No No No No No No No


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Categories: [Polyhedra] [Mathematics-related lists]

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