Fossil polygon patterns - confusing and revealing
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This display of fossil network-like patterns of quite different origin is meant as a warning not to lightsomely misinterpret polygonal meshes as plant cells as it has been done repeatedly in palaeobotany. Among the patterns seen here, only one shows cells. Three of them are crack patterns in silicified peat, without any relation to the peat texture. The remaining three are related to nematophytes in different ways, which makes them relevant for solving the problem of where to place these enigmatic organisms on the tree of life.
stomata pseudo cells Nematothallus
cracks in silicified peat peat cracks Cosmochlaina

columnar cracks in silicified layered peat

Fig.1: Epidermis with stomata, well visible in the incident light reflected from the slanting crack face below,
        Asteroxylon, Lower Devonian, Rhynie chert.
Fig.2: Nematophyte in Rhynie chert, apparently consisting of parallel tubes with thick coatings of gel
        width of the picture 0.7mm.
Fig.3: Enigmatic "Nematothallus cuticle", often found together with carbonaceous nematophyte compressions,
        width of the picture 0.05mm.

Figs.4,5,7: mm-size polyhedra and polygonal columns in silicified peat, seen as polygonal networks on the cut face,
        Lower Permian, Döhlen basin, Germany.
Fig.6: "Cosmochlaina cuticle" [1], interpreted as a crack pattern here.

Apparently the sample in Fig.2 is the only one found hitherto which leads the way to an understanding of both Nematothallus (Fig.3) and Cosmochlaina (Fig.6), the Silurian /Lower Devonian cuticles whose attempted interpretations as being related to the epidermis of some plant had been in vain. Although the patterns in Fig.3 and Fig.6 are quite different, there are reasons to assume that both are replicas of shrinkage crack patterns on the surface of a lump of organic gel harbouring the tubular structure of a nematophyte.
Obviously the pattern in Fig.6, unlike the one in Fig.3, does not follow the boundaries of the gel coats squeezed into more or less polygonal columns as in Fig.2 but resembles the polygonal cracks in Figs.4,5,7 instead.
The irregular polyhedra in Figs.4,5,7 may be elongated, with length /diameter ratios exceeding 20, and thus can be considered analogous to the well-known big basalt columns [5].
The present interpretation of Fig.6 contradicts a recent interpretation as the lower epidermis of a hypothetical ancient liverwort [2], thereby refuting the hypothesis by
Graham et al. [3] which reduces Prototaxites to a liverwort carpet roll.
Addendum 2016:
The above images, of course, represent only a small fraction of polygonal or polyhedral patterns encountered in connection with fossils. Polygons of biological origin are the less problematic ones: When individual globular cells join, in the course of evolution, to make a tightly knit tissue, they necessarily become polyhedral, as they are in the tissue of land plants (Fig.1). Even more easily understood are aligned coated cylinders whose coatings become squeezed into columns with polygonal cross-section, as in Fig.2.
More problematic are the polygons and polyhedra formed by propagating cracks. Since crack propagation is governed by fracture mechanics, one might expect mechanics to provide easy explanations. It has turned out, however, that only simplified model crack configurations can be shown to develop along the lines of fracture mechanics into networks of regular meshes. The extension of such results to more real situations, as here in Figs.4-7, may be called justified guesswork.

Samples:  Figs.1,2,4,5: own finds, Fig.1: photograph by H. Sahm; Fig.3: photograph by H. Kerp, in [4].
                Fig.7:  found and photographed by Wolfgang Schwarz.

H.-J. Weiss     2012        completed 2014

[1]  D. Edwards: Dispersed cuticles of putative non-vascular plants from the Lower Devonian of Britain,
      Bot. J. Linnean Soc. 93(1986), 259-75.
[2]  L.E. Graham, L.W. Wilcox, M.E. Cook, P.G. Gensel:
      Resistant tissues of modern marchantoid liverworts resemble enigmatic Early Paleozoic microfossils.
      Proc. Nat. Acad. Sci., USA, 101(2004), 11025-29.  
[3]  L.E. Graham, M.E. Cook, D.T. Hanson, K.B. Pigg, J.M. Graham :
     Structural, physiological, and stable carbon isotope evidence that the enigmatic Paleozoic fossil Prototaxites formed from rolled liverwort mats.
     Am. J. Bot. 97(2010), 268-275.
[4]  H. Steur, W.v.d. Brugghen: Grondboor & Hamer (1998), 28-35.
[5]  M. Hofmann et al.: Why hexagonal basalt columns ? Phys. Rev. Lett. 115, 154301 (2015).

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