Studies into Polyhedra - Johnson

Look around the Graphics Lab

Regular, Semi-Regular Polyhedra, and thier Duals (first page)
Prisms, Anti-prisms, Pryamids, and related Polyhedra
Miscellanous Polyhedra: Deltahedra
Johnson Solids -- The other convex polyhedra with regular faces

Why I studied polyhedra, and Image Generation Techniques
Known Polyhedral Mathematical Formula
Data Sources and links for Polyhedral Data

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, (augmention) if it remains convex.
• joining various cupolas together in various ways

And so on. Also includes are the two remaining semi-regualar 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	j02_pentagonal_pyramid off vrml	j03_triangular_cupola off vrml
j04_square_cupola off vrml	j05_pentagonal_cupola off vrml	j06_pentagonal_rotunda off vrml
j07_elongated_triangular_pyramid off vrml	j08_elongated_square_pyramid off vrml	j09_elongated_pentagonal_pyramid off vrml

j10_gyroelongated_square_pyramid off vrml	j11_gyroelongated_pentagonal_pyramid off vrml

j12_triangular_dipyramid off vrml	j13_pentagonal_dipyramid off vrml	j14_elongated_triangular_dipyramid off vrml

j15_elongated_square_dipyramid off vrml	j16_elongated_pentagonal_dipyramid off vrml

j17_gyroelongated_square_dipyramid off vrml	j18_elongated_triangular_cupola off vrml
j19_elongated_square_cupola off vrml	j20_elongated_pentagonal_cupola off vrml
j21_elongated_pentagonal_rotunds off vrml	j22_gyroelongated_triangular_cupola off vrml
j23_gyroelongated_square_cupola off vrml	j24_gyroelongated_pentagonal_cupola off vrml

j25_gyroelongated_pentagonal_rotunda off vrml	j26_gyrobifastigium off vrml	j27_triangular_orthobicupola off vrml

j28_square_orthobicupola off vrml	j29_square_gyrobicupola off vrml	j30_pentagonal_orthobicupola off vrml

j31_pentagonal_gyrobicupola off vrml	j32_pentagonal_orthocupolarontunda off vrml	j33_pentagonal_gyrocupolarotunda off vrml

j34_pentagonal_orthobirotunda off vrml	j35_elongated_triangular_orthobicupola off vrml
j36_elongated_triangular_gyrobicupola off vrml	j37_elongated_square_gyrobicupola off vrml
j38_elongated_pentagonal_orthobicupola off vrml	j39_elongated_pentagonal_gyrobicupola off vrml
j40_elongated_pentagonal_orthocupolarotunda off vrml	j41_elongated_pentagonal_gyrocupolarotunda off vrml
j42_elongated_pentagonal_orthobirotunda off vrml	j43_elongated_pentagonal_gyrobirotunda off vrml
j44_gyroelongated_triangular_bicupola off vrml	j45_gyroelongated_square_bicupola off vrml
j46_gyroelongated_pentagonal_bicupola off vrml	j47_gyroelongated_pentagonal_cupolarotunda off vrml
j48_gyroelongated_pentagonal_birotunda off vrml	j49_augmented_triangular_prism off vrml
j50_biaugmented_triangular_prism off vrml	j51_triaugmented_triangular_prism off vrml
j52_augmented_pentagonal_prism off vrml	j53_biaugmented_pentagonal_prism off vrml
j54_augmented_hexagonal_prism off vrml	j55_parabiaugmented_hexagonal_prism off vrml
j56_metabiaugmented_hexagonal_prism off vrml	j57_triaugmented_hexagonal_prism off vrml
j58_augmented_dodecahedron off vrml	j59_parabiaugmented_dodecahedron off vrml
j60_metabiaugmented_dodecahedron off vrml	j61_triaugmented_dodecahedron off vrml
j62_metabidiminished_icosahedron off vrml	j63_tridiminished_icosahedron off vrml
j64_augmented_tridiminished_icosahedron off vrml	j65_augmented_truncated_tetrahedron off vrml
j66_augmented_truncated_cube off vrml	j67_biaugmented_truncated_cube off vrml
j68_augmented_truncated_dodecahedron off vrml	j69_parabiaugmented_truncated_dodecahedron off vrml
j70_metabiaugmented_truncated_dodecahedron off vrml	j71_triaugmented_truncated_dodecahedron off vrml
j72_gyrate_rhombicosidodecahedron off vrml	j73_parabigyrate_rhombicosidodecahedron off vrml
j74_metabigyrate_rhombicosidodecahedron off vrml	j75_trigyrate_rhombicosidodecahedron off vrml
j76_diminished_rhombicosidodecahedron off vrml	j77_paragyrate_diminished_rhombicosidodecahedron off vrml

j78_metagyrate_diminished_rhombicosidodecahedron off vrml

j79_bigyrate_diminished_rhombicosidodecahedron off vrml	j80_parabidiminished_rhombicosidodecahedron off vrml

j81_metabidiminished_rhombicosidodecahedron off vrml	j82_gyrate_bidiminished_rhombicosidodecahedron off vrml

j83_tridiminished_rhombicosidodecahedron off vrml

j84_snub_disphenoid off vrml	j85_snub_square_antiprism off vrml

j86_sphenocorona off vrml	j87_augmented_sphenocorona off vrml	j88_sphenomegacorona off vrml

j89_hebesphenomegacorona off vrml	j90_disphenocingulum off vrml
j91_bilunabirotunda off vrml	j92_triangular_hebesphenorotunda off vrml