Higher-$n$ triangular dilatonic black holes

Dilaton gravity with the form fields is known to possess dyon solutions with two horizons for the discrete (“triangular”) values of the dilaton coupling constant $a=\sqrt{n(n+1)\mathrm{/}2}$. From this sequence only $n=1,2$ members were known analytically so far. We present two new $n=3,5$ triangular solutions for the theory with different dilaton couplings $a,b$ in electric and magnetic sectors in which case the quantization condition reads $a b = n (n

• 1)/2$\mathrm{.}ThesearederivedviatheTodachainsfor$B_2$and$G_2$ Lie algebras. Solutions are found in the closed form in general $D$ space-time dimensions. They satisfy the entropy product rules and have negative binding energy in the extremal case.