![[C36 molecule: `lumpy']](images/lumpy.jpg)
Also with 36 vertices are the two smallest forms with no symmetries at all (one shown).
![[C36 molecule: `barrel']](images/barrel.jpg)
![[C36 molecule: `false barrel']](images/falseb.jpg)
The first fullerene smaller than C60 to be isolated was C36
(eight hexagons). This has 15 theoretical forms (not counting
reflections). I'd bet what they found were the two which are
smoother than any smaller form, having no vertices where three
pentagons meet; I call them "barrel" and "false
barrel".
The true barrel has one sixfold axis, six twofold axes and seven reflection planes.
The false barrel has three twofold axes and two reflection planes.
(I know it shouldn't be skewed like that.
I'm rewriting my model in hopes that that degree of freedom will go away.)
Also with 36 vertices are the two smallest forms with no symmetries at all (one shown).
(Images made with POV-Ray 3.0 or 3.1)
See also: Fullerene gallery: uses Java to rotate any of 1249 forms up to C52. I can't easily visualize 3d structure from these stick images, but maybe you can.
My raw list of 3958 solutions up to C58 (19 hexagons).
2003 Jun 20: I've just learned from George Hart that this class of figures was first described by one Michael Goldberg: ``A Class of Multi-Symmetric Polyhedra,'' Tohoku Mathematics Journal, 43, 1937, pp. 104-108.
index page created 1998 Sep 10; this page spun off from it 1999 Nov 21