The notions of regularity and characteristic width of detonation cells are revisited based on crossed analyses of experimental head-on and longitudinal recordings obtained with the soot-plate technique. Tubes with cross-sections of different shapes, namely round, triangular and square, but the same surface area of 16 cm 2 , are used to detonate the stable mixture 2 H 2 + O 2 + 2 Ar at the initial temperature T 0 = 294 K and the initial pressure p 0 varying from 15 kPa to 100 kPa. The longitudinal recordings show the well-known regular arrangements for this mixture for all cross-section shapes and p 0 , but those on the head-on recordings are irregular except for the square shape and low-enough p 0. There are fewer cells in the round tube, more in the square one, and their average widths and relative differences increase with decreasing p 0. All head-on cells become irregular and independent on the cross-section shapes with increasing p 0. In the square tube, the modulation of the cell phase shift suggests that randomly distributed phenomena with characteristic times at least the actual reaction time add up to compressibility, chemical kinetics and tube geometry. The cellular dynamics at the walls of a tube is thus not representative of that on the whole detonation front, and longitudinal soot traces alone are not sufficient for describing the cellular structure. An analysis based on elements of graph theory proposes that a tessellation of regular hexagons can model a large set of irregular head-on cells. This defines an average cell width from a cell count an experimental head-on recording and an intrinsic but high minimum error on the cell width. Its resulting oversensitivity to the parameters of the simplest Arrhenius rate of chemical evolution indicates that detailed schemes of chemical kinetics and more advanced conceptual tools than a single length are necessary for characterizing the three-dimensional patterns of detonation cells. The Voronoi tessellation supplemented with a physical criterion for the surface density of randomly-distributed point sources could represent a step forward.