This paper ‘with code’ presents several notable properties of the matrix U shown to be related to the isomorphism between H4 and E8. The most significant of these properties is that U.U is to rank 8 matrices what the golden ratio is to numbers. That is to say, the difference between it and its inverse is the identity element, albeit with a twist. Specifically, U.U-(U.U)−1 is the reverse identity matrix or standard involutory permutation matrix of rank 8. It has the same palindromic characteristic polynomial coefficients as the normalized 3-qubit Hadamard matrix with 8-bit binary basis states, which is known to be isomorphic to E8 through its (8,4) Hamming code. This combined with finding the construction of U from the Pauli matrices’ relationships to 2-qubit CNOT, SWAP and 3-qubit Toffoli CCNOT and Hadamard matrices will inform the understanding of group theoretic quantum mechanics (QM), quantum computing (QC), quantum chemistry, and particle physics.