Dihedron/Equilateral triangle/Matrix description/Action on vertices/Exercise

We consider an equilateral triangle in the ${}x,y$-plane, with ${}(0,0)$ as center and with ${}(1,0)$ as one vertex. Let ${}D$ denote the bipyramid over this triangle with upper top ${}(0,0,2)$ and lower top ${}(0,0,-2)$.

a) Determine the matrices and the rotation axes of the (proper) symmetries that transform ${}D$ to itself.

b) Determine an operation table for these symmetries.

c) Describe what happens to the three vertices of the triangle under these symmetries.

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