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Explore

  • Geometric Models-Regular-Faced Convex Polyhedra
  • Platonic Solids
  • Archimedean Solids, Prisms, and Antiprisms
  • Johnson Solids
  • References

Geometric Models

Johnson Solids

American History Museum

Besides the regular and semiregular solids, there are just ninety-two other convex polyhedra with regular faces. In 1966, the American mathematician Norman W. Johnson, a student of H.S.M. Coxeter at the University of Toronto in Canada, enumerated them. These polyhedra are sometimes called the Johnson solids. In 1969, the Russian Viktor A. Zalgaller offered a computer-based computational proof that Johnson had completed the enumeration of convex polyhedra with regular faces.


Polyhedron Model by Martin Berman, Elongated Triangular Gyrobicupola

Polyhedron Model by Martin Berman, Elongated Square Gyrobicupola

Polyhedron Model by Martin Berman, Elongated Pentagonal Orthobicupola

Polyhedron Model by Martin Berman, Elongated Pentagonal Gyrobicupola

Polyhedron Model by Martin Berman, Elongated Pentagonal Orthocupolarotunda

Polyhedron Model by Martin Berman, Elongated Pentagonal Gyrocupolarotunda

Polyhedron Model by Martin Berman, Elongated Pentagonal Orthobirotunda

Polyhedron Model by Martin Berman, Elongated Pentagonal Gyrobirotunda

Polyhedron Model by Martin Berman, Gyroelongated Triangular Bicupola

Polyhedron Model by Martin Berman, Gyroelongated Square Bicupola

Polyhedron Model by Martin Berman, Gyroelongated Pentagonal Bicupola

Polyhedron Model by Martin Berman, Gyroelongated Pentagonal Cupolarotunda

Polyhedron Model by Martin Berman, Gyroelongated Pentagonal Birotunda

Polyhedron Model by Martin Berman, Augmented Triangular Prism

Polyhedron Model by Martin Berman, Biaugmented Triangular Prism

Polyhedron Model by Martin Berman, Triaugmented Triangular Prism

Polyhedron Model by Martin Berman, Augmented Pentagonal Prism

Polyhedron Model by Martin Berman, Biaugmented Pentagonal Prism

Polyhedron Model by Martin Berman, Augmented Hexagonal Prism

Polyhedron Model by Martin Berman, Parabiaugmented Hexagonal Prism

Polyhedron Model by Martin Berman, Metabiaugmented Hexagonal Prism

Polyhedron Model by Martin Berman, Triaugmented Hexagonal Prism

Polyhedron Model by Martin Berman, Augmented Dodecahedron

Polyhedron Model by Martin Berman, Parabiaugmented Dodecahedron

Polyhedron Model by Martin Berman, Metabiaugmented Dodecahedron

Polyhedron Model by Martin Berman, Triaugmented Dodecahedron

Polyhedron Model by Martin Berman, Metabidiminished Icosahedron

Polyhedron Model by Martin Berman, Tridiminished Icosahedron

Polyhedron Model by Martin Berman, Augmented Tridiminished Icosahedron

Polyhedron Model by Martin Berman, Augmented Truncated Tetrahedron

Polyhedron Model by Martin Berman, Augmented Truncated Cube

Polyhedron Model by Martin Berman, Biaugmented Truncated Cube

Polyhedron Model by Martin Berman, Augmented Truncated Dodecahedron

Polyhedron Model by Martin Berman, Parabiaugmented Truncated Dodecahedron

Polyhedron Model by Martin Berman, Metabiaugmented Truncated Dodecahedron


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