We have analyzed the isophotal shapes of a sample of 63 elongated elli
ptical galaxies, previously classified E4, 5, 6 or 7. We sorted them a
ccording to their isophotal class, defined by the type of deviations f
rom perfectly elliptical isophotal contours. These deviations are expe
cted to appear clearly, because of the very favorable orientation of t
hese galaxies. We find the following results, after exclusion of 6 non
-elliptical galaxies: A large percentage (56%) of elongated E's are di
sky objects with pointed isophotes, while only 35% have either boxy or
irregular isophotes, in equal proportions, and the remaining 6 galaxi
es (10%) are difficult to classify. Furthermore, 38% of disky E's also
show slightly boxy spheroids. In almost all the galaxies of the sampl
e, there is an angular range where the deviations are of the disk-type
. The four galaxies not showing this effect are among the roundest one
s of the sample, which suggests that projection effects hide detailed
structures of this kind in many ellipticals. The correlations already
reported in the literature between isophotal class and radio, X-ray em
ission and kinematical behavior are confirmed. In particular, there is
a clear-cut correlation between velocity anisotropy and isophotal sha
pe. The most elongated Hubble types tend to be disky E's. Boxy/irregul
ar E's rarely exceed ellipticities of 0.45 while the maximum elliptici
ty of half of the disky E's exceeds this value. These results confirm
the dichotomy of E's, which fall roughly into two classes, disky and b
oxy/irregular ellipticals. They also show a physical continuity betwee
n disky E's and SO's and suggest that the Hubble types are strongly co
rrelated with disk-to-bulge ratios throughout the Hubble sequence, eve
n at its early-type end (round E's), for which the disk is hidden by o
rientation effects. Galaxies escaping the correlations are the boxy/ir
regular E's, resulting probably from strong merging processes.