  Quantifying genuine entanglement is a key task in quantum information theory.
We study the quantification of genuine multipartite entanglement for four-qubit
systems. Based on the concurrence of nine different classes of four-qubit
states, with each class being closed under stochastic local operation and
classical communication, we construct a concurrence tetrahedron. Proper genuine
four-qubit entanglement measure is presented by using the volume of the
concurrence tetrahedron. For non genuine entangled pure states, the four-qubit
entanglement measure classifies the bi-separable entanglement. We show that the
concurrence tetrahedron based measure of genuine four-qubit entanglement is not
equivalent to the genuine four-partite entanglement concurrence. We illustrate
the advantages of the concurrence tetrahedron by detailed examples.
