Studies into Polyhedra - Johnson

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Johnson Solids

Johnson did a complete study of all convex solids built using just edges of equal length, and regular polygonal faces. All such objects have been found and those not mentioned above have been logically named, and given a 'J' index number.

Johnson solids are named by taking the various Platonic and Archimedian Solids, and performing various operations on them, including...

• Cutting the solid into parts along co-planar edges (cutting off cupolas, and leaving a diminished object)
• Twisting the object along co-planar edges (gyro-rotation)
• Inserting a layer of squares (elongation) or triangles (gyro-elongation) along co-planar edges.
• Adding pyramids onto faces, (augmentation) if it remains convex.
• joining various cupolas together in various ways
And so on. Also includes are the two remaining semi-regular pyramids, and bi-pyramids, though not prisms, or anti-prisms (gyro-prisms) of which their are an infinite number. He also found some extremely weird looking objects, that are really impossible to describe. Note that duals, and di-pyramids (or dual-prisms) are not part of this series as the edges of these objects are not all of equal length, or have irregular polygonal faces.

 j01_square_pyramid off   vrml wikipedia j02_pentagonal_pyramid off   vrml wikipedia j03_triangular_cupola off   vrml wikipedia j04_square_cupola off   vrml wikipedia j05_pentagonal_cupola off   vrml wikipedia j06_pentagonal_rotunda off   vrml wikipedia j07_elongated_triangular_pyramid off   vrml wikipedia j08_elongated_square_pyramid off   vrml wikipedia j09_elongated_pentagonal_pyramid off   vrml wikipedia
 j10_gyroelongated_square_pyramid off   vrml wikipedia j11_gyroelongated_pentagonal_pyramid off   vrml wikipedia
 j12_triangular_dipyramid off   vrml wikipedia j13_pentagonal_dipyramid off   vrml wikipedia j14_elongated_triangular_dipyramid off   vrml wikipedia
 j15_elongated_square_dipyramid off   vrml wikipedia j16_elongated_pentagonal_dipyramid off   vrml wikipedia
 j17_gyroelongated_square_dipyramid off   vrml wikipedia j18_elongated_triangular_cupola off   vrml wikipedia j19_elongated_square_cupola off   vrml wikipedia j20_elongated_pentagonal_cupola off   vrml wikipedia j21_elongated_pentagonal_rotunds off   vrml wikipedia j22_gyroelongated_triangular_cupola off   vrml wikipedia j23_gyroelongated_square_cupola off   vrml wikipedia j24_gyroelongated_pentagonal_cupola off   vrml wikipedia
 j25_gyroelongated_pentagonal_rotunda off   vrml wikipedia j26_gyrobifastigium off   vrml wikipedia j27_triangular_orthobicupola off   vrml wikipedia
 j28_square_orthobicupola off   vrml wikipedia j29_square_gyrobicupola off   vrml wikipedia j30_pentagonal_orthobicupola off   vrml wikipedia
 j31_pentagonal_gyrobicupola off   vrml wikipedia j32_pentagonal_orthocupolarontunda off   vrml wikipedia j33_pentagonal_gyrocupolarotunda off   vrml wikipedia
 j34_pentagonal_orthobirotunda off   vrml wikipedia j35_elongated_triangular_orthobicupola off   vrml wikipedia j36_elongated_triangular_gyrobicupola off   vrml wikipedia j37_elongated_square_gyrobicupola off   vrml wikipedia j38_elongated_pentagonal_orthobicupola off   vrml wikipedia j39_elongated_pentagonal_gyrobicupola off   vrml wikipedia j40_elongated_pentagonal_orthocupolarotunda off   vrml wikipedia j41_elongated_pentagonal_gyrocupolarotunda off   vrml wikipedia j42_elongated_pentagonal_orthobirotunda off   vrml wikipedia j43_elongated_pentagonal_gyrobirotunda off   vrml wikipedia j44_gyroelongated_triangular_bicupola off   vrml wikipedia j45_gyroelongated_square_bicupola off   vrml wikipedia j46_gyroelongated_pentagonal_bicupola off   vrml wikipedia j47_gyroelongated_pentagonal_cupolarotunda off   vrml wikipedia j48_gyroelongated_pentagonal_birotunda off   vrml wikipedia j49_augmented_triangular_prism off   vrml wikipedia j50_biaugmented_triangular_prism off   vrml wikipedia j51_triaugmented_triangular_prism off   vrml wikipedia j52_augmented_pentagonal_prism off   vrml wikipedia j53_biaugmented_pentagonal_prism off   vrml wikipedia j54_augmented_hexagonal_prism off   vrml wikipedia j55_parabiaugmented_hexagonal_prism off   vrml wikipedia j56_metabiaugmented_hexagonal_prism off   vrml wikipedia j57_triaugmented_hexagonal_prism off   vrml wikipedia j58_augmented_dodecahedron off   vrml wikipedia j59_parabiaugmented_dodecahedron off   vrml wikipedia j60_metabiaugmented_dodecahedron off   vrml wikipedia j61_triaugmented_dodecahedron off   vrml wikipedia j62_metabidiminished_icosahedron off   vrml wikipedia j63_tridiminished_icosahedron off   vrml wikipedia j64_augmented_tridiminished_icosahedron off   vrml wikipedia j65_augmented_truncated_tetrahedron off   vrml wikipedia j66_augmented_truncated_cube off   vrml wikipedia j67_biaugmented_truncated_cube off   vrml wikipedia j68_augmented_truncated_dodecahedron off   vrml wikipedia j69_parabiaugmented_truncated_dodecahedron off   vrml wikipedia j70_metabiaugmented_truncated_dodecahedron off   vrml wikipedia j71_triaugmented_truncated_dodecahedron off   vrml wikipedia j72_gyrate_rhombicosidodecahedron off   vrml wikipedia j73_parabigyrate_rhombicosidodecahedron off   vrml wikipedia j74_metabigyrate_rhombicosidodecahedron off   vrml wikipedia j75_trigyrate_rhombicosidodecahedron off   vrml wikipedia j76_diminished_rhombicosidodecahedron off   vrml wikipedia j77_paragyrate_diminished_rhombicosidodecahedron off   vrml wikipedia
 j78_metagyrate_diminished_rhombicosidodecahedron off   vrml wikipedia
 j79_bigyrate_diminished_rhombicosidodecahedron off   vrml wikipedia j80_parabidiminished_rhombicosidodecahedron off   vrml wikipedia
 j81_metabidiminished_rhombicosidodecahedron off   vrml wikipedia j82_gyrate_bidiminished_rhombicosidodecahedron off   vrml wikipedia
 j83_tridiminished_rhombicosidodecahedron off   vrml wikipedia
 j84_snub_disphenoid off   vrml wikipedia j85_snub_square_antiprism off   vrml wikipedia
 j86_sphenocorona off   vrml wikipedia j87_augmented_sphenocorona off   vrml wikipedia j88_sphenomegacorona off   vrml wikipedia
 j89_hebesphenomegacorona off   vrml wikipedia j90_disphenocingulum off   vrml wikipedia j91_bilunabirotunda off   vrml wikipedia j92_triangular_hebesphenorotunda off   vrml wikipedia

Created: 30 April 2001
Updated: 18 May 2005
Author: Anthony Thyssen, <anthony@cit.gu.edu.au>
URL: `http://www.cit.gu.edu.au/~anthony/graphics/polyhedra/`