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, (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