Johnson Solids

The term Johnson Solid is used to describe a non-uniform convex polyhedron with regular faces.  The table of all 92 such figures was first published by N.W.Johnson in "Convex Solids with Regular Faces", published in Canadian Journal of Mathematics, Vol 18 pp 169-200 (1966).  The names of the majority of the Johnson Solids were ascribed by Johnson at this time, indeed in a communication dated December 2004, Dr Johnson states 'when I was investigating regular-faced solids in the early 1960s, there were no established names even for many of the obvious ones, except for pyramids and bipyramids.  So I invented terms like "cupola" and "rotunda" and devised other terminology ("augmented," "diminished," "elongated," etc.) that covered all but the eight or nine anomalous figures at the end of my list, which got their own descriptive names.'

The
table below lists all of the Johnson solids.  All links are to HEDRON 'switchable' VRML files.

Polyhedra can also be generated which are isomorphs of the Johnson solids.  In cases where the solid contains a {5}, {8}, or {10}-gon then these can be replaced by {5/2}, {8/3} or {10/3}-gons respectively.  With vertices crossed and the symmetry of the original Jonhson Solid retained, then some of these polyhedra appear to pass the criteria for being prefixed "Great".  I am aware though that this prefix is normally reserved for Uniform Polyhedra.  Where an isomorph exists which does not appear to meet the 'Great' criteria I have tried to give as descriptive a name as possible.  All isomorph names are of my own invention.

Alex Doskey has also introduced a page to his website where he discusses 'Convex Diamond Regular Polyhedra', an extension to the Johnson Solids, Steve Waterman also has a similar page.  Alex and Steve catalogue 70 additional polyhedra which result from allowing one extra polygon, a rhombus formed from two coplanar triangles.

Thanks to Alex Doskey for providing the numbers in the second column.