A comprehensive analysis of intramolecular G-quadruplex (G4) structures has been conducted, revealing key insights into their formalism. Using the ASC-G4 website, 333 intramolecular G4 structures were analyzed, clarifying key concepts and introducing new information. Each of the eight distinguishable topologies corresponds to a groove-width signature and a predominant glycosidic configuration (gc) pattern, determined by the directions of the strands. The relative orientations of the stacking guanines within the strands, quantified and related to their vertical gc successions, determine the twist and tilt of the helices. These factors influence the minimum groove widths, which represent the space available for lateral ligand binding. Despite the importance of the vertical gc succession, it does not have a strict one-to-one relationship with the topology, explaining discrepancies between some topologies and their corresponding circular dichroism (CD) spectra. This study introduced the concept of platypus G4s, which exhibit properties corresponding to multiple topologies. The analysis revealed four types of groove widths, three types of twist angles, and the importance of groove width in ligand binding. The study also showed that the direction of reading the gc succession is important, even though it is not currently correct in the literature. The results demonstrated a correlation between the angles of successive stacking guanines and the twist and tilt angles, which impact the real available space in the grooves for ligand binding. The study also showed that the groove widths are influenced by the direction of the strands, with each topology having a unique groove-width signature. The analysis of the 333 structures revealed that the groove widths are determined by the direction of the strands, with each topology having a unique groove-width signature. The study also showed that the groove widths are influenced by the presence of ligands and proteins, but not significantly when the topology is not modified. The results highlight the importance of groove width in the binding of ligands and proteins to G4 structures. The study also showed that the groove widths are influenced by the presence of discontinuities, such as bulges and snapbacks, but not significantly. The analysis of the 333 structures revealed that the groove widths are determined by the direction of the strands, with each topology having a unique groove-width signature. The study also showed that the groove widths are influenced by the presence of ligands and proteins, but not significantly when the topology is not modified. The results highlight the importance of groove width in the binding of ligands and proteins to G4 structures.A comprehensive analysis of intramolecular G-quadruplex (G4) structures has been conducted, revealing key insights into their formalism. Using the ASC-G4 website, 333 intramolecular G4 structures were analyzed, clarifying key concepts and introducing new information. Each of the eight distinguishable topologies corresponds to a groove-width signature and a predominant glycosidic configuration (gc) pattern, determined by the directions of the strands. The relative orientations of the stacking guanines within the strands, quantified and related to their vertical gc successions, determine the twist and tilt of the helices. These factors influence the minimum groove widths, which represent the space available for lateral ligand binding. Despite the importance of the vertical gc succession, it does not have a strict one-to-one relationship with the topology, explaining discrepancies between some topologies and their corresponding circular dichroism (CD) spectra. This study introduced the concept of platypus G4s, which exhibit properties corresponding to multiple topologies. The analysis revealed four types of groove widths, three types of twist angles, and the importance of groove width in ligand binding. The study also showed that the direction of reading the gc succession is important, even though it is not currently correct in the literature. The results demonstrated a correlation between the angles of successive stacking guanines and the twist and tilt angles, which impact the real available space in the grooves for ligand binding. The study also showed that the groove widths are influenced by the direction of the strands, with each topology having a unique groove-width signature. The analysis of the 333 structures revealed that the groove widths are determined by the direction of the strands, with each topology having a unique groove-width signature. The study also showed that the groove widths are influenced by the presence of ligands and proteins, but not significantly when the topology is not modified. The results highlight the importance of groove width in the binding of ligands and proteins to G4 structures. The study also showed that the groove widths are influenced by the presence of discontinuities, such as bulges and snapbacks, but not significantly. The analysis of the 333 structures revealed that the groove widths are determined by the direction of the strands, with each topology having a unique groove-width signature. The study also showed that the groove widths are influenced by the presence of ligands and proteins, but not significantly when the topology is not modified. The results highlight the importance of groove width in the binding of ligands and proteins to G4 structures.