#### Dissection protocol

The pelvi-femoral complex was removed from all corpses between the third lumbar vertebra and the tibio-femoral joint. Soft tissues were cut away. At the coxo-femoral joint the articular capsule was cut and the femoral head was removed from the acetabular cavity while taking care to avoid damage to the labrum. An anatomical preparation with an intact labrum was obtained. Four stainless-steel nails with a diameter of 1 mm were implanted in each hip bone in order to generate a three-dimensional system of reference landmarks. The bone was pierced by means of a 0.9-mm-diameter drill and stainless-steel nails were placed in the holes. The nails were implanted, on the one hand, with a maximal dispersion relative to the overall pelvic volume to produce an accurate three-dimensional system and, on the other hand, in the thickest parts of the bones, for example the iliac tubercle and the pelvic brim, to avoid their disassembly during the study period.

Digitalisations were performed using a MicroScribe^{®} G2 (Immersion, France) with a precision of ± 0.38 mm according to the constructor. Three-dimensional coordinates (*x*, *y*, *z*) were recorded in a millimetric orthonormal reference system.

For each hip bone, the pelvis was immobilised in a clamp and the coordinates of the four nails (reference landmarks) were digitised in the centre of the nail head. The apex of the labrum, i.e. its free margin, was acquired by recording coordinates of successive points (Fig. 2A) using the MicroScribe programmed to take coordinates 1 mm apart. These acquisitions had to be done shortly after the opening of the articular capsule to prevent desiccation of the labrum, which would cause the loss of its natural shape.

To test the intra- and inter-observer measurement errors, this digitising protocol was repeated six times by one observer and three times by a second observer on eight acetabula.

#### Osteological treatments

After dissections the pelves were collected and cleaned by osteological treatments performed by the technician of the SPOT (Service de Préparations Ostéologiques et Taxidermiques) of the National Museum of Natural History of Paris (France). The osteological preparation consisted of different baths of alcohol, enzymatic digestion and drying. These treatments did not affect the nails position. To test for potential bone deformation induced by osteological preparation, the six Euclidian distances between the four nails of each hip bone were computed and compared before and after preparation. Given a precision of the Microscribe^{®} G2 at 0.38 mm and a nail diameter of 1 mm, we fixed the threshold for error due to protocol-induced measurement error at twice the instrument precision, i.e. 0.76 mm. Differences between distances obtained on isolated bones before and after preparation never reached 0.76 mm, implying no bone deformation during osteological preparations.

#### Data collection on dry bones

On dry bones, a new anatomical description of the acetabular rim was performed. The acetabular rim, interrupted by the acetabular notch, is limited by the anterior and posterior horn tips (indicated, respectively, by A and D in Fig. 1). Two inflexions were systematically identified: a most cranial inflexion (Fabeck et al. 1998), where the indentation of the anterior part of the rim appears (B in Fig. 1); and a most caudal inflexion, which was placed at the beginning of the posterior horn curve (C in Fig. 1). They were used to divide the acetabular rim in two parts, named anterior and posterior acetabular rims.

New data acquisitions were performed on osteological specimens. The hip bone was immobilised in a clamp and the three-dimensional coordinates of the four nails were recorded.

Successive points, using the MicroScribe programmed to take coordinates 1 mm apart, were digitised along the totality of the acetabular rim (from A to D in Fig. 1, resulting in Fig. 2B), along its posterior part only (from B to C resulting in Fig. 2C), and along its anterior part only (from A to B and from C to D resulting in Fig. 2D). Successive points were also acquired along the edges of the *facies lunata*, the articular surface of the acetabulum taking a characteristic horseshoe shape. Finally, the three-dimensional coordinates of the homologous landmarks corresponding to the anatomical points A–D (Fig. 1) were recorded, as well as the two landmarks corresponding to the insertion of the ilium and the ichium on the acetabular rim (respectively, 1 and 2 in Fig. 1).

The digitising protocol was repeated six times by one observer and three times by a second observer on eight acetabula to test intra- and inter-observer errors.

#### Data processing

Regression planes, using the least squares method, were computed based on the points acquired on the entire dry acetabular rim (Fig. 2B), on the posterior rim only (Fig. 2C) and on the anterior rim only (Fig. 2D), resulting in three planes (a_{i}*x* + b_{i}*y* + c_{i}*z* + d_{i} = 0), which were named, respectively, P_{T} (total plane), P_{P} (posterior plane) and P_{A} (anterior plane). For each plane, the standard deviation (SD), i.e. the mean of the distance of each point from the regression plane, was computed. A Fligner–Killeen test was computed to compare the values of the standard deviation obtained based on P_{T} and the mean value of the standard deviations obtained based on the two planes P_{P} and P_{A}.

The regression plane based on the points acquired on the labrum (Fig. 2A) was computed, resulting in the plane P_{L} (labrum plane). In summary, we obtained four planes P_{T}, P_{P}, P_{A} and P_{L} combined with their respective direction vector (a_{i}, b_{i}, c_{i}) named V_{T}, V_{P}, V_{A} and V_{L}. A methodological problem in the reconstruction of the vector V_{A} was observed. To obtain more accurate data, we decided to reconstruct the plane of the anterior rim using a regression based on the three points A–C (large points in Fig. 2D) rather than on the successive points acquired on the anterior part of the acetabular rim. This methodological choice is described and explained in the discussion. A new plane P_{A2} was thus calculated combined with its direction vector V_{A2}.

To evaluate the intra- and inter-observer measurement errors, the regression planes were computed on each repetition performed by the first and second observers on eight acetabula. A mean vector of the six direction vectors obtained by the first observer and a mean vector of the three direction vectors obtained by the second observer were calculated. The intra-observer measurement error corresponds to the mean angle between the mean vector obtained by the first observer and each direction vector of his six repetitions. The inter-observer measurement error corresponds to the angle between the mean vector obtained by the first observer and the mean vector obtained by the second observer.

To analyse the different three-dimensional orientations of the labrum and the posterior and anterior rims, the angles between V_{L}, V_{A2} and V_{P} were computed for each acetabulum. First, both linear least squared regressions and correlation tests, using the Pearson method, were calculated on the different angles. Moreover, anovas were performed to test the laterality, sex and age effects on the three angles. These three angles are interdependent, requiring the Bonferroni correction. Second, the coplanarity of the vectors V_{L}, V_{A2} and V_{P} was tested. The three angles between these vectors served to compute the percentages of the two smaller angles in comparison with the greater angle. If the sum of these two percentages equalled to 100%, the coplanarity of the three vectors was concluded and a new plane P_{C} (convergence plane) was established combined with its direction vector V_{C}.

The mean height of the labrum and the acetabular rim in relation to the acetabular centre were also analysed. A regression sphere computed based on the points acquired on the edge of the *facies lunata* served to obtain the coordinates of the acetabular centre O. This point O was projected, first, in P_{L} and, second, in P_{T}, allowing to obtain the mean height of the labrum and the acetabular rim in relation with the acetabular centre. A negative value was attributed when the plane passed below O, a positive value when the plane passed above O. Correlation tests were performed between these two heights and, first, the orientation of V_{L}, V_{A2} and V_{P} and, second, the age.

The three-dimensional orientation of P_{C} was explored in relation with the more general anatomy of the acetabular region. The two landmarks acquired at the intersection between the acetabular rim and, first, the ilium (landmark 1 in Fig. 1) and, second, the ischium (landmark 2 in Fig. 1) served to compute the axis (*D*). Moreover, the vector OA between the acetabular centre and the point A was calculated. Both the angle between V_{C} and (*D*) and the angle between V_{C} and OA served to analyse the orientation of P_{C} in the acetabular region. anovas were performed to test the laterality, sex and age effects on the orientation of P_{C}.