  We measure the geometry of a crumpled sheet of paper with laser-aided
topography and discuss its statistical properties. The curvature of an
elasto-plastic fold scales linearly with applied force. The curvature
distribution follows an exponential form with regions of high curvature
localized along ridges. The measured ridge length distribution is consistent
with a hierarchical model for ridge breaking during crumpling. A large fraction
of the ridges are observed to terminate without bifurcating and the ridge
network connectedness is not as complete as anticipated. The self-affinity of
the surface is characterized by a Hurst exponent of $0.72\pm 0.01$ in contrast
with previous results.
