G-quadruplexes (G4) are helical structures found in guanine-rich DNA or RNA sequences. Generally, their formalism is based on a few dozen structures, which can produce some inconsistencies or incompleteness. Using the website ASC-G4, we analyzed the structures of 333 intramolecular G4s, of all types, which allowed us to clarify some key concepts and present new information. To each of the eight distinguishable topologies corresponds a groove-width signature and a predominant glycosidic configuration (gc) pattern governed by the directions of the strands. The relative orientations of the stacking guanines within the strands, which we quantified and related to their vertical gc successions, determine the twist and tilt of the helices. The latter impact the minimum groove widths, which represent the space available for lateral ligand binding. The G4 four helices have similar twists, even when these twists are irregular, meaning that they have various angles along the strands. Despite its importance, the vertical gc succession has no strict one-to-one relationship with the topology, which explains the discrepancy between some topologies and their corresponding circular dichroism spectra. This study allowed us to introduce the new concept of platypus G4s, which are structures with properties corresponding to several topologies.