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 partially degraded exine ofPinus griffithiiMcClell., 3.0 Å diameter molecular units were observed with fivefold symmetry. Using the modified Markham rotation method, secondary points of symmetry were also observed indicating that the quasi-crystalloid organization is at the molecular level. 2. In the partially degraded and fragmented wall ofBotryococcus brauniiKütz., obtained from fossil colonies extracted from the Hungarian Oil Shale, two kinds of biopolymer structures were observed in the same fragment. One type was a quasi-equivalent globular unit with a diameter of 50–75 Å, whereas the other type consisted of peculiar quasi-crystalloid pentagonal polygons with a diameter of 20–30 Å. Symmetry operations involving the points of the biopolymer structured wall of the fossilBotryococcusalgae were made for the first time. A quasi-crystalloid skeleton was also demonstrated as present in this cell wall. 3. A three dimensional model of the sporoderm quasi-crystalloid skeleton was established. A complete model of the Penrose-II type biopolymer structure is presented here. This model contains 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”,sensuNelson 1986, are also asymmetrical with a peculiar asymmetry which can be observed in this large biopolymer model.