A regular tetrahedron is constructed within a unit cube in such a way that its four vertices coincide with those of the cube – see the diagram.

**Question Alpha**

What is the volume of the tetrahedron?

**Question Omega**

If you have been following this week’s questions, then you’ll find the above pretty simple. So, let’s increase the difficulty dial! Imagine constructing another regular tetrahedron using the other four vertices of the unit cube. The space where the two tetrahedra overlap is known as the core. What is the name of the polyhedral core? What is the volume of this core?

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Enjoy!

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**This PMQ16 competition closes on MONDAY 29 April at 23:59 GMT - one extra weekday from now on**.

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