This paper presents new, direct surface measurements on irregular particles including 69 crushed and 18 naturally rounded rocks (37.5-4.75 mm ASTM sieve designation). A three-dimensional laser scanner (LS) was used to obtain the coordinates of points on the surface of the rocks and to estimate their volume, surface area, and density. The test results were compared with those of two other measurement approaches: classical projected area method (PAM) and modern X-ray computed tomography (CT), which were performed on the same suite of rocks. The results of LS and CT agree well with respect to volume and surface area. A polar representation was chosen to study the variation of geometrical properties of rocks. Relationships between geometrical characteristics and shape of rocks were further studied using surface curvatures and related parameters (e.g. chord length and caliper diameter). The measurement results were then examined using some longstanding geometrical conjectures that formerly have been inaccessible owing to lack of data. (C) 2011 Elsevier B.V. All rights reserved.