Amrik Sen, Raymond Aschheim, and Klee Irwin (2017)

We present the emergence of a root system in six dimensions from the tetrahedra of an icosahedral core known as the 20-group (20G) within the framework of Clifford’s geometric algebra. Consequently, we establish a connection between a three-dimensional icosahedral seed, a six-dimensional (6D) Dirichlet quantized host and a higher dimensional lattice structure. The 20G, owing to its icosahedral symmetry, bears the signature of a 6D lattice that manifests in the Dirichlet integer representation. We present an interpretation whereby the three-dimensional 20G can be regarded as the core substratum from which the higher dimensional lattices emerge. This emergent geometry is based on an induction principle supported by the Clifford multi-vector formalism of three-dimensional (3D) Euclidean space. This lays a geometric framework for understanding several physics theories related to $SU(5)$, $E_{6}$, $E_8$ Lie algebras and their composition with the algebra associated with the even unimodular lattice in $R^{3,1}$. The construction presented here is inspired by Penrose’s three world mode.