The enamels of advanced cimolodontan multituberculate teeth from the Paleocene Bug Creek Anthills locality in Montana were found to be prismatic.63 It was later hypothesized that members of the suborder Taeniolabidoidea64 had enamel with exceptionally widely spaced prisms never seen before in fossil or extant mammalian enamels, whereas members of the suborder Ptilodontoidea had enamels consisting of small prisms like all other known extinct or extant mammalian enamels. The exceptional taeniolabidoid enamel was called “gigantoprismatic”.65 This hypothesis was confirmed independently seven years later by one North American team66, 67 and one European team.68

In enamel formation of extant mammals, the closely apposed columnar ameloblasts are hexagonally arranged in cross sections planoparallel with the ameloblast/enamel contact surface. Each ameloblast produces one prism rod and half the thickness of its surrounding interprismatic enamel. Therefore, the prisms are also hexagonally distributed in such sectional planes. The enamel prisms run from the dentin−enamel junction to the outer surface of the enamel mantle.69, 70 Hunter−Schreger bands seen in longitudinal sections characterize their centrifugal course in most mammalian enamels.71 Fig. 18 is a diagrammatic description of prismatic enamel in a section tangential to the enamel surface. The prisms are represented by hexagonally distributed circles. The hexagon in the lower left corner represents the cross-sectional secretory area of one ameloblast producing a prism and half the thickness of interprismatic enamel along its peripheral rim. It is evident that there are as many contiguous hexagons with common sides as circles in the diagram. Such hexagons cannot easily be delineated and measured in a less regular prism pattern. However, the area of a tetragon with its corners in the centers of four adjacent cross-cut prisms equals the secretory area of one ameloblast, since there are as many contiguous tetragons as prisms in such a distributional pattern.72 It is not difficult to plot approximate geometrical centers of cross−cut prisms. The area of each tetragon is the sum of the areas of the two triangles formed by the shorter diagonal. The area of a tetragon is thus easily calculated. One mm2 divided by the mean tetragon area expresses the number of prisms per mm2 and thus also the original ameloblast number per mm2.73 The diameters of the prisms are without consequence for these values. Prismatic diameters vary independently from central distances between prisms and only reflect diameters of Tome’s processes inameloblasts.74, 75, 76

In Fig. 19, showing planed and etched enamel of the cimolodontan multituberculate Meniscoessus sp., the scale bar in the original photo represents 10 μm and measured 40 mm. The linear magnification was thus 4000x. The mean length of the sides of the traced pair of adjoining triangles constituting the tetragon in the original photo was 61.5 mm. The following proportion is then valid:
	10/40 = d/61.5.
	Thus d = (10 * 61.5)/40 = 15.375 μm,
d being the true length of the mean triangle side, hence called central distance (CD), in the Meniscoessus enamel in Fig. 19. The number of cross−cut prisms per mm2 is given by the general equation:
	a = (2*106) / (d2*3½)
where a is the number of prisms per mm2. The exponent “½” signifies square root. For the Meniscoessus specimen, the numerical prism density in the micrographed enamel location is 4884/mm2.

For any enamel, the calculated mean CD and number of prisms/mm2 are never exact values but good statistical approximations. Only in small enamel areas are cross-cut prisms regularly arranged as in Fig. 19. The numerical prism density is ideally computed by the mean tetragon area defined by the sides in a pair of triangles joined by one common side.77 However, the average CD is less time consuming to calculate and use; this method was first applied by Carlson and Krause.79 The results are close to and do not seem to deviate systematically from the density calculated by the mean tetragon area expressed by the contiguous triangles of the measured enamel surface.

When only four given cross-cut adjacent prisms, describing one tetragon, are used for calculation, the errors in plotting centers and measuring the central distances will be greater than if several contiguous tetragons are traced.80

Except the untreated Bolodon crassidens enamel in Fig. 23, the following enamel micrographs depict planed and etched surfaces planoparallel with the natural outer enamel surface and have been presented in separate earlier publications by the author.

Gigantoprismatic enamels have until now been observed in numerous multituberculates.85 In the superfamily Ptilodontoidea, normal prismatic enamels seem characteristic, as well as in many other known extant and extinct mammals.86, 87, 88, 89 Central distances in gigantoprismatic enamel imply ameloblast diameters that have never been seen in any extant vertebrate. Moreover, to my knowledge, no other secretory columnar epithelium with such large cells is known elsewhere in the body of extant mammals. Therefore, it is safe to maintain that the gigantoprismatic enamel demonstrates a unique anatomical character in mammalian evolution.

The montage in Fig. 20 demonstrates the difference between gigantoprismatic and normal prismatic enamel. The magnification is the same in A and B, and, in both micrographs, the centers of 12 adjacent prisms have been connected in groups, each forming a continuous cluster of 12 triangles. The difference in size is obvious, but less striking than in many other comparisons between normal and gigantoprismatic enamels with identical magnification. Clusters of triangles describe more accurately the mean CD, the marginal errors in plotting and measuring single, separate triangles being reduced significantly. The drawn triangle clusters in A and B need not necessarily be identical with those used by calculation in the original micrographs.

Fig. 21 graphically demonstrates qualitatively the probability that gigantoprismatic enamels form their own morphological “class” or universe. To firmly support this supposition statistically, each single value should have been qualified by its standard deviation. To obtain this, deeper planing and thus more destructive methods would have been necessary. However, the variation in mean numerical prism densities did not seem significantly different in the two enamel types.

Recently, some authors, including myself, have used the term “microprismatic” for ptilodontoid and most other mammalian enamels. This might imply that there is also a medium prism size. Therefore, all nontaeniolabidoid90 enamels should be designated “normal.”

Whether the different crystal aggregates (prisms?) shown in Fig. 22 have had a relation to original ameloblasts like normal prisms and continue into the enamel below the micrographed surface is questionable. A more superficial planed and etched enamel surface planoparallel to the one in Fig. 22 in the same tooth was also micrographed and showed a much higher relative number of the smaller crystal bodies.91 Thus, there seems to be no point in calculating their numerical density since a corresponding variation in cell size (CD) within a population of enamel-producing ameloblasts is improbable. Enamel etching lasted maximally 5 secs using 5% HNO3 and was always interupted by rinsing in pure water.92, 93 Recrystallization after etching is, therefore, very improbable as no precipitation could occur, and it is no more probable than for the derived cimolodontan enamels. Clusters of bodies of the same size and distribution as the larger structures in Fig. 22 were also seen in unplaned and unetched enamels by incident light microscopy in this and other specimens of Purbeck multituberculates (Fig. 23). Furthermore, size and distribution of prisms are identical using SEM techniques with etching or with polarized light microscopy without etching.95, 96 Thus Jurassic plagiaulacidan enamels in plesiomorphic and geologically older multituberculates deserve a closer, more invasive examination regarding the continuity of possible structures from inner to outer enamel surface, to compare with more derived multituberculate enamel forms. Also, an important aim is to describe micromorphological evolutionary stages between the types represented in Figs. 20 and 22.