This week I posted the last of the Johnson solids on my website. To commemorate this landmark event, I created a family portrait of the Johnson solids:

(High resolution version available from the
Johnson solids page. Enjoy!!!)
This image actually shows 97 rather than 92 solids, because the 5 chiral Johnson solids are paired with their respective mirror-images.
This particular layout has some very neat coincidences:
I didn't want to relegate the crown jewels to the far back of the image, since they are among the most interesting and unique of the Johnson solids; so I decided to put them in the front. There are 9 of them, and following them are the 6 basic prismatic solids (the pyramids and cupolae). So this suggests the breakdown 4+5 followed by 6, thus leading to the truncated triangular arrangement you see above. Since 4 + 5 + 6 + ... is just the difference of two triangular numbers, in particular T(n) - T(3), and it so happens that T(14) - T(3) = 99, that means the first 10 rows can follow the formation of T(13) - T(3) = 85, then the last row can repeat the 3rd last row of 12 elements, thus maintaining the hexagonal packing and forming a truncated triangular boundary.
And it just so happens that since the crown jewels were moved to the front, the last row of 12 solids exactly coincided with the modifications of the rhombicosidodecahedron -- they all fit in exactly one row.
This triangular layout is also a nice layout for the perspective projection of the camera, so that everything fits nicely in the 3D scene.
Another coincidence is that J26, the gyrobifastigium, appears more-or-less in the center of the layout, being the unique digonal cupola derivative counted among the Johnson solids.
Originally, I had only 92 solids in the layout, but that led to an ugly last row. Adding in the 5 enantiomers of J44-J48 pushed the total up to 97, exactly T(3)+2 short of T(15)=105, thus allowing for the present nice, symmetrical layout.
P.S., I've derived / found from published papers exact algebraic coordinates for all of the Johnson solids, from which arbitrary-precision coordinate values may be obtained. They are posted on the respective Johnson solid's page on my website, so if you ever have a research project that required exact coordinates for the Johnson solids, now you know where to find them.
