Johnson's polyhedra

A Johnson's polyhedron is convex with regular faces - thus all its edges have same length - which is neither regular or archimedean, nor a prism or an anti-prism. There are 92. You get most of them by modifying pyramids, regular or archimedean solids, prisms or anti-prisms:
prisms, cupolas and rotunda (J1-6), modified pyramids and dipyramids (J7-17), modified cupolas and rotundas (J18-48), augmented prisms ((J49-57), modified Platonic solids J58-64), modified Archimedes solids (J65-83), various (J84-92).
J37 is the only one whose vertices are superimposables (order 4, three squares and one triangle).
Only five are chiral (exist in two mirror image versions) : the gyroelongated polyhedra (modified by inserting an antiprism in the place of a facet) J44-48.

The table below shows their complete list in the order defined by Johnson, with the numbers of faces and vertices of each type (fn is a regular polygon with n sides, and p faces and p edges meet at a vertex vp).

name (with link to popup applet)   Jnn faces - vertices   image face's colors: f3 f4 f5 f6 f8 f10	square pyramid   J01 4f3 1f5 - 4v3 1v4	pentagonal pyramid   J02 5f3 1f5 - 5v3 1v5
triangular cupola   J03 4f3 3f4 1f6 - 6v3 3v4	square cupola   J04 4f3 5f4 1f8 - 8v3 4v4	pentagonal cupola   J05 5f3 5f4 1f5 1f10 - 10v3 5v4
pentagonal rotunda   J06 10f3 6f5 1f10 - 10v3 10v4	elongated triangular pyramid   J07 4f3 3f4 - 4v3 3v4	elongated square pyramid   J08 4f3 5f4 - 4v3 5v4
elongated pentagonal pyramid   J09 5f3 5f4 1f5 - 5v3 5v4 1v5	gyroelongated square pyramid   J10 12f3 1f4 - 5v4 4v5	gyroelongated pentagonal pyramid   J11 15f3 1f5 - 5v4 6v5
triangular dipyramid   J12 6f3 - 2v3 3v4	pentagonal dipyramid   J13 10f3 - 5v4 2v5	elongated triangular dipyramid   J14 6f3 3f4 - 2v3 6v4
elongated square dipyramid   J15 8f3 4f4 - 10v4	elongated pentagonal dipyramid   J16 10f3 5f4 - 10v4 2v5	gyroelongated square dipyramid   J17 16f3 - 2v4 8v5
elongated triangular cupola   J18 4f3 9f4 1f6 - 6v3 9v4	elongated square cupola   J19 4f3 13f4 1f8 - 8v3 12v4	elongated pentagonal cupola   J20 5f3 15f4 1f5 1f10 - 10v3 15v4
elongated pentagonal rotunda   J21 10f3 10f4 6f5 1f10 - 10v3 20v4	gyroelongated triangular cupola   J22 16f3 3f4 1f6 - 9v4 6v5	gyroelongated square cupola   J23 20f3 5f4 1f8 - 12v4 8v5
gyroelongated pentagonal cupola   J24 25f3 5f4 1f5 1f10 - 15v4 10v5	gyroelongated pentagonal rotunda   J25 25f3 5f4 1f5 1f10 - 15v4 10v5	triangular gyrobiprism   J26 4f3 4f4 - 4v3 4v4
triangular orthobicupola   J27 8f3 6f4 - 12v4	square orthobicupola   J28 8f3 10f4 - 16v4	square gyrobicupola   J29 8f3 10f4 - 16v4
pentagonal orthobicupola   J30 10f3 10f4 2f5 - 20v4	pentagonal gyrobicupola   J31 10f3 10f4 2f5 - 20v4	pentagonal orthocupolarotunda   J32 15f3 5f4 7f5 - 25v4
pentagonal gyrocupolarotunda   J33 15f3 5f4 7f5 - 25v4	pentagonal orthobirotunda   J34 20f3 12f5 - 30v4	elongated triangular orthobicupola   J35 8f3 12f4 - 18v4
elongated triangular gyrobicupola   J36 8f3 12f4 - 18v4	elongated square gyrobicupola   J37 8f3 18f4 - 24v4	elongated pentagonal orthobicupola   J38 10f3 20f4 2f5 - 30v4
elongated pentagonal gyrobicupola   J39 10f3 20f4 2f5 - 30v4	elongated pentag. orthocupolarotunda   J40 15f3 15f4 7f5 - 35v4	elongated pentag. gyrocupolarotunda   J41 15f3 15f4 7f5 - 35v4
elongated pentagonal orthobirotunda   J42 20f3 10f4 12f5 - 40v4	elongated pentagonal gyrobirotunda   J43 20f3 10f4 12f5 - 40v4	gyroelongated triangular bicupola   J44 20f3 6f4 - 6v4 12v5
gyroelongated square bicupola   J45 24f3 10f4 - 8v4 16v5	gyroelongated pentagonal bicupola   J46 30f3 10f4 2f5 - 10v4 20v5	gyroelongated pentag. cupolarotunda   J47 35f3 5f4 7f5 - 15v4 20v5
gyroelongated pentag. birotunda   J48 40f3 12f5 - 20v4 20v5	augmented triangular prism   J49 6f3 2f4 - 2v3 5v4	biaugmented triangular prism   J50 10f3 1f4 - 6v4 2v5
triaugmented triangular prism   J51 14f3 - 3v4 6v5	augmented pentagonal prism   J52 4f3 4f4 2f5 - 6v3 5v4	biaugmented pentagonal prism   J53 8f3 3f4 2f5 - 2v3 10v4
augmented hexagonal prism   J54 4f3 5f4 2f6 - 8v3 5v4	parabiaugmented hexagonal prism   J55 8f3 4f4 2f6 - 4v3 10v4	metabiaugmented hexagonal prism   J56 8f3 4f4 2f6 - 4v3 10v4
triaugmented hexagonal prism   J57 12f3 3f4 2f6 - 15v4	augmented dodecahedron   J58 5f3 11f5 - 15v3 5v4 1v5	parabiaugmented dodecahedron   J59 10f3 10f5 - 10v3 10v4 2v5
metabiaugmented dodecahedron   J60 10f3 10f5 - 10v3 10v4 2v5	triaugmented dodecahedron   J61 15f3 9f5 - 5v3 15v4 3v5	metabidiminished icosahedron   J62 10f3 2f5 - 2v3 6v4 2v5
tridiminished icosahedron   J63 5f3 3f5 - 6v3 3v4	augmented tridiminished icosahedron   J64 7f3 3f5 - 4v3 6v4	augmented truncated tetrahedron   J65 8f3 3f4 3f6 - 6v3 9v4
augmented truncated cube   J66 12f3 5f4 5f8 - 16v3 12v4	biaugmented truncated cube   J67 16f3 10f4 4f8 - 8v3 24v4	augmented truncated dodecahedron   J68 25f3 5f4 1f5 11f10 - 50v3 15v4
parabiaugmented trunc. dodecahedron   J69 30f3 10f4 2f5 10f10 - 40v3 30v4	metabiaugmented trunc. dodecahedron   J70 30f3 10f4 2f5 10f10 - 40v3 30v4	triaugmented trunc. dodecahedron   J71 35f3 15f4 3f5 9f10 - 30v3 45v4
gyrate rhombicosidodecahedron   J72 20f3 30f4 12f5 - 60v4	parabigyrate rhombicosidodecahedron   J73 20f3 30f4 12f5 - 60v4	metabigyrate rhombicosidodec.   J74 20f3 30f4 12f5 - 60v4
trigyrate rhombicosidodecahedron   J75 20f3 30f4 12f5 - 60v4	diminished rhombicosidodecahedron   J76 15f3 25f4 11f5 1f10 - 10v3 45v4	paragyrate dimin. rhombicosidodec.   J77 15f3 25f4 11f5 1f10 - 10v3 45v4
metagyrate dimin. rhombicosidodec.   J78 15f3 25f4 11f5 1f10 - 10v3 45v4	bigyrate diminished rhombicosidodec.   J79 15f3 25f4 11f5 1f10 - 10v3 45v4	parabidiminished rhombicosidodec.   J80 10f3 20f4 10f5 2f10 - 20v3 30v4
metabidiminished rhombicosidodec.   J81 10f3 20f4 10f5 2f10 - 20v3 30v4	gyrate bidiminished rhombicosidodec.   J82 10f3 20f4 10f5 2f10 - 20v3 30v4	tridiminished rhombicosidodecahedron   J83 5f3 15f4 9f5 3f10 - 30v3 15v4
snub disphenoid   J84 12f3 - 4v4 4v5	snub square antiprism   J85 24f3 2f4 - 16v5	sphenocorona   J86 12f3 2f4 - 6v4 4v5
augmented sphenocorona   J87 16f3 1f4 - 3v4 8v5	sphenomegacorona   J88 16f3 2f4 - 4v4 8v5	hebesphenomegacorona   J89 18f3 3f4 - 4v4 10v5
disphenocingulum   J90 20f3 4f4 - 4v4 12v5	bilunabirotunda   J91 8f3 2f4 4f5 - 4v3 10v4	triangular hebesphenorotunda   J92 13f3 3f4 3f5 1f6 - 18v4

These images and the data for the applets have been produce using Hedron, the polyhedra software by Jim McNeill (label "Wales" on the link globe).

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November 1998 updated 24-08-2009