A symmetrical Heyting algebra is an algebra \((A;\land,\lor,',\Rightarrow,0,1)\) such that \((A;\land,\lor,\Rightarrow,0,1)\) is a Heyting algebra and \((A;\land,\lor,',0,1)\) is a DeMorgan algebra. The Heyting algebra is \(I_ n\)-symmetrical if it satisfies the Ivo Thomas equality. The authors show that these algebras are semi-simple. They characterize simple algebras and their subalgebras and answer a problem raised by A. Monteiro.