Geometric Aspects of Pollen: Polyhedrons (Vernonieae – Asteraceae), Rotated Symmetry (Trichanthereae – Acanthaceae) and Pyramidal to Prismatic Spinules (Nothapodytes – Icacinaceae)

Abstract

Three special types of pollen geometric aspects, the polyhedric lophate-lacunar grains of the Asteraceae, the 2-colporate rotated symmetric grains of the Acanthaceae, and the pyramidal to prismatic spinules of the Icacinaceae are discussed in this report. The lacunar patterns in four types (Adenoon indicum Type, Vernonia anthelmintica Type-1 & Type-2, and Vernonia monosis Type) of 3-colpororate pollen are described by simple mathematical formulae. This evidence shows that the lacunar patterns of lophate grains are controlled by the geometry of spherical surface configurations. The occurrence of two types of lacunar patterns of lophate pollen within a taxon, V. anthelmintica, is supportive of our hypothesis that a few reversible lacunar changes involving addition or suppression of our hypothesis that a few reversible lacunar changes involving addition or suppression of crosswalls may bring about different lacunar patterns. With regard to the 2-colporate rotated symmetric pollen of the tribe Trichanthereae, we underscore here that its physical equilibrium is maintained despite rotation, by the equal number of foveoreticulate bands and a colporus in each rotated hemisphere. The angular spinules are unique as they differ from the common coniform type of pollen spines and spinules. These geometric exine patterns are morphologically distinctive, with differences that can be described mathematically. As such, they provide potentially useful data for phylogenetic analysis.