The structure of the <i>C</i>₆₀ molecule.

<p>(a) The polytope is formed by 60 vertices equidistant from its center. Its surface consists of 12 regular pentagons and 20 regular hexagons. All 90 edges are of the same length. (b) The polytope viewed in the direction almost parallel to the plane spanned by and , which makes the orbits (pentagons and decagons) easy to identify. (c) The polytope viewed in the direction parallel to the plane spanned by and . Surface edges of are omitted in (b) and (c). Horizontal segments are projections of the orbits. The number in a row shows the coordinate of the orbit. The vertical direction is that of .</p

The structure of the <i>C</i>₇₀ molecule.

<p>(a) The polytope has 105 edges and 12 pentagonal and 25 hexagonal faces. (b) viewed from a direction almost parallel to the plane of and . (c) The structure of viewed from a direction parallel to the plane of and . The column of numbers shows the -coordinate of the orbits of vertices of . The inserted decagon has the -coordinate equal to 0. Surface edges are omitted in (b) and (c).</p

A ring of hexagons from the middle of the surface of

<p><b> and </b><b> unwrapped into the plane.</b> Horizontal lines indicate positions of the four decagons in and five decagons in . The dominant points identify the decagons relative to the basis . Dashed lines are the boundaries of the ring of five inserted hexagons.</p

The 12 pentagons of the surface of

<p><b> are shown without the hexagons.</b> The 60 dots are the vertices of . The polytope is oriented as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084079#pone-0084079-g001" target="_blank">Fig. 1</a>.</p