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Polyhedron's subclasses include icosahedron, prism, square pyramid, Triangular dipyramid and Pentagonal dipyramid.

prism (a polyhedron with two congruent and parallel faces (the bases) and whose lateral faces are parallelograms)

triangular dipyramid, a first in the infinite set of face-transitive dipyramids

arrangement of edge-joined polygons in the plane which can be folded to become the faces of the polyhedron

Deltoidal icositetrahedron

deltoidal icositetrahedron, a Catalan solid which looks a bit like an overinflated cube

Disdyakis dodecahedron

disdyakis dodecahedron, or hexakis octahedron, a Catalan solid and the dual to the Archimedean truncated cuboctahedron

Deltoidal hexecontahedron

deltoidal hexecontahedron, a catalan solid which looks a bit like an overinflated dodecahedron

disdyakis triacontahedron, or hexakis icosahedron, a Catalan solid and the dual to the Archimedean truncated icosidodecahedron

triakis icosahedron

triakis icosahedron, an Archimedean dual solid, or a Catalan solid

Pentagonal icositetrahedron

pentagonal icositetrahedron, a catalan solid which is the dual of the snub cube

gyroelongated pentagonal pyramid

gyroelongated pentagonal pyramid, one of the Johnson solids

Pentagonal orthobirotunda

pentagonal orthobirotunda, one of the Johnson solids

gyroelongated square cupola

gyroelongated square cupola, one of the Johnson solids

pentagonal pyramid, a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point

Gyroelongated square dipyramid

gyroelongated square dipyramid, one of the Johnson solids

Elongated square dipyramid

elongated square dipyramid, one of the Johnson solids

Pentagonal hexecontahedron

pentagonal hexecontahedron, a Catalan solid, dual of the snub dodecahedron

triakis tetrahedron

triakis tetrahedron, an Archimedean dual solid, or a Catalan solid

triakis octahedron

triakis octahedron, an Archimedean dual solid, or a Catalan solid

snub disphenoid

snub disphenoid, one of the Johnson solids

triaugmented triangular prism

triaugmented triangular prism, one of the Johnson solids

square cupola

square cupola, one of the Johnson solids

Pentagonal cupola

pentagonal cupola, one of the Johnson solids

triangular cupola

triangular cupola, one of the Johnson solids

triangular orthobicupola

triangular orthobicupola, one of the Johnson solids

elongated pentagonal pyramid

elongated pentagonal pyramid, one of the Johnson solids

Heronian tetrahedron

Heronian tetrahedron, a tetrahedron whose sides, faces and volume, all rational numbers

elongated triangular cupola

elongated triangular cupola, one of the Johnson solids

elongated square pyramid

elongated square pyramid, one of the Johnson solids

Bilunabirotunda

bilunabirotunda, one of the Johnson solids

Gyrate rhombicosidodecahedron

Gyrate rhombicosidodecahedron, one of the Johnson solids

Triangular hebesphenorotunda

triangular hebesphenorotunda, one of the Johnson solids

Augmented pentagonal prism

augmented pentagonal prism, one of the Johnson solids

Augmented hexagonal prism

augmented hexagonal prism, one of the Johnson solids

Gyrate bidiminished rhombicosidodecahedron

gyrate bidiminished rhombicosidodecahedron, one of the Johnson solids

gyroelongated triangular cupola

gyroelongated triangular cupola, one of the Johnson solids

Augmented truncated tetrahedron

augmented truncated tetrahedron, one of the Johnson solids

tridiminished rhombicosidodecahedron

Tridiminished rhombicosidodecahedron, one of the Johnson solids

Metabigyrate rhombicosidodecahedron

metabigyrate rhombicosidodecahedron, one of the Johnson solids

tridiminished icosahedron

Tridiminished icosahedron, one of the Johnson solids

Triaugmented hexagonal prism

triaugmented hexagonal prism, one of the Johnson solids

Parabigyrate rhombicosidodecahedron

parabigyrate rhombicosidodecahedron, one of the Johnson solids

Disphenocingulum

Disphenocingulum, one of the Johnson solids

gyroelongated square pyramid

gyroelongated square pyramid, one of the Johnson solids

square orthobicupola

square orthobicupola, one of the Johnson solids

Metabidiminished icosahedron

Metabidiminished icosahedron, one of the Johnson solids

gyroelongated pentagonal bicupola

gyroelongated pentagonal bicupola, one of the Johnson solids

Bigyrate diminished rhombicosidodecahedron

bigyrate diminished rhombicosidodecahedron, one of the Johnson solids

elongated pentagonal orthocupolarotunda

elongated pentagonal orthocupolarotunda, one of the Johnson solids

Gyroelongated triangular bicupola

gyroelongated triangular bicupola, one of the Johnson solids

Parabiaugmented hexagonal prism

parabiaugmented hexagonal prism, one of the Johnson solids

elongated square cupola

elongated square cupola, one of the Johnson solids

Sphenomegacorona

Sphenomegacorona, one of the Johnson solids

Pentagonal orthocupolarotunda

pentagonal orthocupolarotunda, one of the Johnson solids

Biaugmented pentagonal prism

biaugmented pentagonal prism, one of the Johnson solids

Augmented sphenocorona

Augmented sphenocorona, one of the Johnson solids, and is obtained by adding a square pyramid to one of the square faces of the sphenocorona

pentagonal gyrobicupola

pentagonal gyrobicupola, one of the Johnson solids

Metabiaugmented hexagonal prism

metabiaugmented hexagonal prism, one of the Johnson solids

Augmented triangular prism

augmented triangular prism, one of the Johnson solids

Biaugmented triangular prism

biaugmented triangular prism, one of the Johnson solids

elongated triangular orthobicupola

elongated triangular orthobicupola, one of the Johnson solids

Gyroelongated pentagonal rotunda

gyroelongated pentagonal rotunda, one of the Johnson solids

Trigyrate rhombicosidodecahedron

Trigyrate rhombicosidodecahedron, one of the Johnson solids

gyroelongated square bicupola

gyroelongated square bicupola, one of the Johnson solids

elongated pentagonal gyrocupolarotunda

elongated pentagonal gyrocupolarotunda, one of the Johnson solids

pentagonal orthobicupola

pentagonal orthobicupola, one of the Johnson solids

Snub square antiprism

snub square antiprism, one of the Johnson solids

Augmented tridiminished icosahedron

augmented tridiminished icosahedron, one of the Johnson solids

Augmented dodecahedron

augmented dodecahedron, one of the Johnson solids

gyroelongated pentagonal birotunda

gyroelongated pentagonal birotunda, one of the Johnson solids

elongated pentagonal rotunda

elongated pentagonal rotunda, one of the Johnson solids

square gyrobicupola

square gyrobicupola, one of the Johnson solids

elongated pentagonal orthobirotunda

elongated pentagonal orthobirotunda, one of the Johnson solids

Parabidiminished rhombicosidodecahedron

Parabidiminished rhombicosidodecahedron, one of the Johnson solids

Elongated pentagonal gyrobirotunda

elongated pentagonal gyrobirotunda, one of the Johnson solids

Metabiaugmented dodecahedron

metabiaugmented dodecahedron, one of the Johnson solids

Pentagonal gyrocupolarotunda

pentagonal gyrocupolarotunda, one of the Johnson solids

Elongated pentagonal gyrobicupola

elongated pentagonal gyrobicupola, one of the Johnson solids

elongated triangular gyrobicupola

elongated triangular gyrobicupola, one of the Johnson solids

Paragyrate diminished rhombicosidodecahedron

paragyrate diminished rhombicosidodecahedron, one of the Johnson solids

gyroelongated pentagonal cupolarotunda

gyroelongated pentagonal cupolarotunda, one of the Johnson solids

Metabidiminished rhombicosidodecahedron

Metabidiminished rhombicosidodecahedron, one of the Johnson solids

elongated pentagonal orthobicupola

elongated pentagonal orthobicupola, one of the Johnson solids

Elongated triangular dipyramid

elongated triangular dipyramid, one of the Johnson solids

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