  In this paper we study the issue of the puzzle of the radii of calcium
isotopes. Despite an excess of eight neutrons, strangely $^{48}{\rm Ca}$
exhibits essentially the same charge radius as $^{40}{\rm Ca}$ does. A
fundamental microscopic description of this is still lacking. Also strange is a
peak in charge radius of calcium at N = 24. The $^{52}{\rm Ca}$ (N = 32)
nucleus, well known to be doubly magical, amazingly has recently been found to
have a very large charge radius. Also amazing is the property of
$^{42}_{14}{\rm Si}_{28}$ which simultaneously appears to be both
magical/spherical and strongly deformed as well. We use a Quantum
Chromodynamics based model, which treats triton as elementary entity to make up
$^{42}_{14}{\rm Si}_{28}$. We show here how this QCD based model is able to
provide a consistent physical understanding of simultaneity of
magicity/sphericity and strong deformation of a single nucleus. This brings in
an essential duality in the structure of $^{42}_{14}{\rm Si}_{28}$ and
subsequently also that of $^{48}_{20}{\rm Ca}_{28}$ We also provide consistent
understanding of the puzzling radii of calcium isotopes. We predict that the
radius of $^{54}{\rm Ca}$ should be even bigger than that of $^{52}{\rm Ca}$;
and also that the radius of $^{60}{\rm Ca}$ should be the same as that of
$^{40}{\rm Ca}$. In addition we also show wherefrom arises the neutron E2
effective charge of $\frac{1}{2}$.
