  Generally the dynamical state of superclusters is poorly known. We study
properties of superclusters and select a sample of quasi-spherical
superclusters, the dynamics of which can be studied using the $\Lambda$
significance diagram. We extracted our supercluster sample with an adaptive
local threshold density method from the Sloan Digital Sky Survey Data Release 7
(SDSS DR7) data and estimated their masses using the dynamical masses for
member galaxies and groups. We used topological analysis based on Minkowski
functionals and the positions of galaxies and galaxy groups in superclusters.
Finally, we highlight the dynamical state of a few exceptional types of
superclusters found in this study using the $\Lambda$ significance diagram. Our
final sample contains 65 superclusters in the distance range of 130 to 450 Mpc.
Supercluster masses range between $1.1 \times 10^{15} M_{\sun}$ and $1.4 \times
10^{16} M_{\sun}$ and sizes between 25 Mpc and 87 Mpc. We find that
pancake-type superclusters form the low-luminosity, small, poor and low-mass
end of superclusters. We find four superclusters of unusual types, exhibiting
exceptionally spherical shapes. These so-called quasi-spherical systems contain
a high-density core surrounded by a relatively spherical density and galaxy
distribution.The mass-to-light ratio of these quasi-sphericals is higher than
those of the other superclusters, suggesting a relatively high dark matter
content. Using the $\Lambda$ significance diagram for oblate and prolate
spheroids, we find that three quasi-spherical superclusters are gravitationally
bound at the present epoch. Quasi-spherical superclusters are among the largest
gravitationally bound systems found to date, and form a special class of giant
systems that, dynamically, are in between large gravitationally unbound
superclusters and clusters of galaxies in an equilibrium configuration.
