Log-optimal (

We enumerate and classify all stationary logarithmic configurations of d + 2 d+2 points on the unit sphere in alttext="d"> encoding="application/x-tex">d –dimensions. In particular, we show that energy attains its local minima at consist two orthogonal to each other regular simplexes cardinality alttext="m"> m encoding="application/x-tex">m alttext="n"> n encoding="application/x-tex">n . The global minimum occurs when alttext="m equals n"> = encoding="application/x-tex">m=n if is even n 1"> 1 encoding="application/x-tex">m=n+1 otherwise. This characterizes a new class minimize alttext="double-struck upper S Superscript d minus S − encoding="application/x-tex">\mathbb {S}^{d-1} for classes known literature, simplex (d+1 ) cross-polytope alttext="2 d"> encoding="application/x-tex">2d ), are both universally optimal configurations.