of pre-merging in 2-d, 3-d, and 4-d. With the '<a
href="qh-optq.htm#Qx">Qx</a>' option, it does a good job in
higher dimensions. In 5-d and higher, Qhull does poorly at
detecting redundant vertices.

<p>In the summary ('<a href="qh-opto.htm#s">s</a>'), look at the
ratio between the maximum facet width and the maximum width of a
single merge, e.g., &quot;(3.4x)&quot;. Qhull usually reports a
ratio of four or lower in 3-d and six or lower in 4-d. If it
reports a ratio greater than 10, this may indicate an
imp