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Polyhedra Notes

written by Rene K. Mueller, Copyright (c) 2007, last updated Wed, January 9, 2008

Johnson Solids

In 1966 Norman Johnson published a paper "Convex Solids with Regular Faces" (Canadian Journal of Mathematics, Vol. 18, 1966, pp. 169-200) in which he classified and named 92 types of convex polyhedra which are composed by same side length additionally to the platonic and archimedean solids:

Square Pyramid

Pentagonal Pyramid

Triangular Cupola

Square Cupola

Pentagonal Cupola

Pentagonal Rotunda

Elongated Triangular Pyramid

Elongated Square Pyramid

Elongated Pentagonal Pyramid

Gyroelongated Square Pyramid

Gyroelongated Pentagonal Pyramid

Triangular Dipyramid

Pentagonal Dipyramid

Elongated Triangular Dipyramid

Elongated Square Dipyramid

Elongated Pentagonal Dipyramid

Gyroelongated Square Dipyramid

Elongated Triangular Cupola

Elongated Square Cupola

Elongated Pentagonal Cupola

Elongated Pentagonal Rotunda

Gyroelongated Triangular Cupola

Gyroelongated Square Cupola

Gyroelongated Pentagonal Cupola

Gyroelongated Pentagonal Rotunda


Triangular Orthobicupola

Square Orthobicupola

Square Gyrobicupola

Pentagonal Orthobicupola

Pentagonal Gyrobicupola

Pentagonal Orthocupolarontunda

Pentagonal Gyrocupolarotunda

Pentagonal Orthobirotunda

Elongated Triangular Orthobicupola

Elongated Triangular Gyrobicupola

Elongated Square Gyrobicupola

Elongated Pentagonal Orthobicupola

Elongated Pentagonal Gyrobicupola

Elongated Pentagonal Orthocupolarotunda

Elongated Pentagonal Gyrocupolarotunda

Elongated Pentagonal Orthobirotunda

Elongated Pentagonal Gyrobirotunda

Gyroelongated Triangular Bicupola

Gyroelongated Square Bicupola

Gyroelongated Pentagonal Bicupola

Gyroelongated Pentagonal Cupolarotunda

Gyroelongated Pentagonal Birotunda

Augmented Triangular Prism

Biaugmented Triangular Prism

Triaugmented Triangular Prism

Augmented Pentagonal Prism

Biaugmented Pentagonal Prism

Augmented Hexagonal Prism

Parabiaugmented Hexagonal Prism

Metabiaugmented Hexagonal Prism

Triaugmented Hexagonal Prism

Augmented Dodecahedron

Parabiaugmented Dodecahedron

Metabiaugmented Dodecahedron

Triaugmented Dodecahedron

Metabidiminished Icosahedron

Tridiminished Icosahedron

Augmented Tridiminished Icosahedron

Augmented Truncated Tetrahedron

Augmented Truncated Cube

Biaugmented Truncated Cube

Augmented Truncated Dodecahedron

Parabiaugmented Truncated Dodecahedron

Metabiaugmented Truncated Dodecahedron

Triaugmented Truncated Dodecahedron

Gyrate Rhombicosidodecahedron

Parabigyrate Rhombicosidodecahedron

Metabigyrate Rhombicosidodecahedron

Trigyrate Rhombicosidodecahedron

Diminished Rhombicosidodecahedron

Paragyrate Diminished Rhombicosidodecahedron

Metagyrate Diminished Rhombicosidodecahedron

Bigyrate Diminished Rhombicosidodecahedron

Parabidiminished Rhombicosidodecahedron

Metabidiminished Rhombicosidodecahedron

Gyrate Bidiminished Rhombicosidodecahedron

Tridiminished Rhombicosidodecahedron

Snub Disphenoid

Snub Square Antiprism


Augmented Sphenocorona





Triangular Hebesphenorotunda

As the time goes by I will comment those forms which look promising for a temporary building.

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