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. 2014 Jul 8;9(7):e102123.
doi: 10.1371/journal.pone.0102123. eCollection 2014.

Fullerene-based symmetry in Hibiscus rosa-sinensis pollen

Kleber Andrade  1 , Sara Guerra  1 , Alexis Debut  1
Affiliations

Fullerene-based symmetry in Hibiscus rosa-sinensis pollen

Kleber Andrade et al. PLoS One. .

Abstract

The fullerene molecule belongs to the so-called super materials. The compound is interesting due to its spherical configuration where atoms occupy positions forming a mechanically stable structure. We first demonstrate that pollen of Hibiscus rosa-sinensis has a strong symmetry regarding the distribution of its spines over the spherical grain. These spines form spherical hexagons and pentagons. The distance between atoms in fullerene is explained applying principles of flat, spherical, and spatial geometry, based on Euclid's "Elements" book, as well as logic algorithms. Measurements of the pollen grain take into account that the true spine lengths, and consequently the real distances between them, are measured to the periphery of each grain. Algorithms are developed to recover the spatial effects lost in 2D photos. There is a clear correspondence between the position of atoms in the fullerene molecule and the position of spines in the pollen grain. In the fullerene the separation gives the idea of equal length bonds which implies perfectly distributed electron clouds while in the pollen grain we suggest that the spines being equally spaced carry an electrical charge originating in forces involved in the pollination process.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Developing phases of Hibiscus rosa-sinensis flower.
A: immature stage, pollen is forming and reproductive organs of the flower are not observed, 1–3 days. B: bud stage, the flower enters in pre-anthesis, 4–5 days. C: anthesis stage, 5–8 days. D: final phase of anthesis, pollen remains viable, 9–12 days. E: senescence phase, flower begins to close, 13–15 days. F: the flower separates from the tree.
Figure 2
Figure 2. Stages of pollen.
A: young stage, pollen grains maintain connections with the anther and the spines are not yet well defined, although they begin to distribute symmetrically over the pollen grains surface. B: adult stage, the pollen has a spherical shape with sharp and long spines. C: old stage, the grain begins to deform, it becomes more vulnerable to treatment for SEM. We identify also that the exine in old stage begins to separate from the surface of pollen, as clearly seen in the picture.
Figure 3
Figure 3. Comparison between an Hibiscus rosa-sinensis grain pollen (A) and a buckminster C60-fullerene molecule (B) (Creative Common License – Rob Hooft).
As seen, both structures present a defined distribution of their elements over the whole surface forming hexagons and pentagons.
Figure 4
Figure 4. Graphical relationship between a hexagon and a pentagon that share an edge.
From this it is possible to calculate what should be the distance between their respective center and vertices (i.e. O 1 Q, O 1 A, O 2 P, O 2 E,…) and the magnitude of their respective apothems O 1 H and O 2 H.
Figure 5
Figure 5. Euclid’s construction showing the length of the corresponding icosahedron inscribed inside the sphere.
To the right is a sketch of the main lines that form the top and bottom of the icosahedron.
Figure 6
Figure 6. Planes that cut icosahedron edges are perpendicular to the radii subtended to their respective vertices.
The edge of the icosahedron is then cut into three segments, the middle one PR is the length edge of the truncated icosahedron or fullerene molecule.
Figure 7
Figure 7. Microphotography of a pollen grain showing angle measurement of some of the spines on its surface.
See this image and copyright information in PMC

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