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Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space

Quantum Gravity Research, Los Angeles, CA 90290, USA
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Academic Editor: Lokenath Debnath
Mathematics 2017, 5(2), 29; https://doi.org/10.3390/math5020029
Received: 23 February 2017 / Revised: 12 May 2017 / Accepted: 18 May 2017 / Published: 26 May 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 S U ( 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 model. View Full-Text
Keywords: aperiodic Dirichlet lattice; icosahedral symmetry; Clifford spinors and Lie algebras aperiodic Dirichlet lattice; icosahedral symmetry; Clifford spinors and Lie algebras
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MDPI and ACS Style

Sen, A.; Aschheim, R.; Irwin, K. Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space. Mathematics 2017, 5, 29. https://doi.org/10.3390/math5020029

AMA Style

Sen A, Aschheim R, Irwin K. Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space. Mathematics. 2017; 5(2):29. https://doi.org/10.3390/math5020029

Chicago/Turabian Style

Sen, Amrik; Aschheim, Raymond; Irwin, Klee. 2017. "Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space" Mathematics 5, no. 2: 29. https://doi.org/10.3390/math5020029

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