This paper presents, for the first time, new information obtained from
a research programme on the biopolymer organization of the sporoderm.
The results are as follows: 1. In the TEM photographs of the partiall
y degraded exine of Pinus griffithii McClell., 3.0 angstrom diameter m
olecular units were observed with fivefold symmetry. Using the modifie
d Markham rotation method, secondary points of symmetry were also obse
rved indicating that the quasi-crystalloid organization is at the mole
cular level. 2. In the partially degraded and fragmented wall of Botry
ococcus braunii Kutz., obtained from fossil colonies extracted from th
e Hungarian Oil Shale, two kinds of biopolymer structures were observe
d in the same fragment. One type was a quasi-equivalent globular unit
with a diameter of 50-75 angstrom, whereas the other type consisted of
peculiar quasi-crystalloid pentagonal polygons with a diameter of 20-
30 angstrom. Symmetry operations involving the points of the biopolyme
r structured wall of the fossil Botryococcus algae were made for the f
irst time. A quasi-crystalloid skeleton was also demonstrated as prese
nt in this cell wall. 3. A three dimensional model of the sporoderm qu
asi-crystalloid skeleton was established. A complete model of the Penr
ose-II type biopolymer structure is presented here. This model contain
s one central unit, surrounded by two types of Penrose-I units. Eight
units can be directly attached to the central unit. An additional six
units may be attached to the previous ones by asymmetrical connections
. The ''large frustrations'', sensu Nelson 1986, are also asymmetrical
with a peculiar asymmetry which can be observed in this large biopoly
mer model.