Question 1118068
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<pre>
The cube has 8 corners, so there are 8 cuts.


Each the cut is a pyramid with three right angled faces.


The orthogonal edges  of the pyramids are {{{1/sqrt(2)}}} = {{{sqrt(2)/2}}} centimeters long each.


So the volume of each pyramid is  V = {{{(1/3)*(1/2)*(sqrt(2)/2)^3}}} = {{{(1/3)*(1/2)*((2*sqrt(2))/8)}}} cubic centimeters.


The total volume of 8 pyramids is  {{{(1/3)*(sqrt(2))}}} cubic centimeters.


The edge of the cube is {{{2*(sqrt(2)/2)}}} = {{{sqrt(2)}}} centimeters.


So the volume of the cube is  {{{(sqrt(2))^3}}} = {{{2*sqrt(2)}}} cubic centimeters.


Then the volume of the solid after cutting the corners of the cube is the difference


{{{2*sqrt(2)}}} - {{{(1/3)*sqrt(2)}}} = {{{(5/3)*sqrt(2)}}} cubic centimeters.


It is your <U>answer</U>.
</pre>

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On  &nbsp;<U>cuboctahedron</U>, &nbsp;see this &nbsp;Wikipedia &nbsp;article


https://en.wikipedia.org/wiki/Cuboctahedron


You will find the Figure there.