What is the phase of matter that has flexible volume, but constant shape?
There is a mathematical argumentative approach called reductio ad absurdum...i.e., bring your own logical reasoning to the point where the result is an absurd statement if you accepted the original statement as true. In this case you can accept that there is a phase which can change its volume but keeps it geometrical shape intacr. You can try disproving your own statement using this method for solids, liquids, and gases.

Do we have a phase of matter that fits in the red cell? In other words, do we have a phase of matter that keeps its shape, and only changes its volume? If so, what is the name of that phase?

a) When solids experience stress, there is strain = deformation, change in volume.
b) Liquids are almost incompressible and they have no shape, but under extreme extreme pressures their volume does change, typically, &gt; 100,000 psi they can become solids. The solid will have the shape of container in which it became a solid.
c) Gases acquire the shape of the container (actually a bad statement, i.e., gases occupy the space provide by the container), and their volume can be easily changed by stress.
d) The fancier state of matter, plasma, it is also an ionized gas, so it does not have a geometrical shape. However, it can be confined by using magnetic fields so that it does not touch the walls of the container, and perhaps its &quot;volume&quot; and &quot;shape&quot; can be manipulated independently. A true physicist can better answer it.