Symmetric 3 Qubit State Invariants

For pure symmetric 3-qubit states there are only three algebraically independent entanglement measures; one choice is the pairwise concurrence $\mathcal{C}$, the 3-tangle $\tau$, and the Kempe invariant $\kappa$. Using a canonical form for symmetric $N$-qubit states derived from their Majorana representation, we derive the explicit achievable region of triples $(\mathcal C,\tau,\kappa)$.