  We show that the quantification of entanglement of any rank-2 state with any
polynomial entanglement measure can be recast as a geometric problem on the
corresponding Bloch sphere. This approach provides novel insight into the
properties of entanglement and allows us to relate different polynomial
measures to each other, simplifying their quantification. In particular,
unveiling and exploiting the geometric structure of the concurrence for two
qubits, we show that the convex roof of any polynomial measure of entanglement
can be quantified exactly for all rank-2 states of an arbitrary number of
qubits which have only one or two unentangled states in their range. We give
explicit examples by quantifying the three-tangle exactly for several
representative classes of three-qubit states. We further show how our methods
can be used to obtain analytical results for entanglement of more complex
states if one can exploit symmetries in their geometric representation.
