Description of facially symmetric spaces with unitary tripotents

We give a description of finite-dimensional real neutral strongly facially symmetric spaces with the property JP. We also prove that if $Z$ is a real neutral strongly facially symmetric with an unitary tripotents, then the space $Z$ is isometrically isomorphic to the space $L_1(\mathrm{\Omega },\mathrm{\Sigma },\mu ),$ where $(\mathrm{\Omega },\mathrm{\Sigma },\mu )$ is a measure space having the direct sum property.