MathDB

Let

C

be a unit cube. Let

D

be a translate of

C

such that one corner of

D

is located at the center of

C

and one corner of

C

is located at the center of

D

. Let

D^\prime

be the image of

D

under a

60^\circ

clockwise rotation about the line that passes through both cube centers when looking from the center of

D

to the center of

C

. What is the volume of the intersection of

C

with

D^\prime

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