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

Amrik Sen, Raymond Aschheim and Klee Irwin
Additional contact information
Amrik Sen: Quantum Gravity Research, Los Angeles, CA 90290, USA
Raymond Aschheim: Quantum Gravity Research, Los Angeles, CA 90290, USA
Klee Irwin: Quantum Gravity Research, Los Angeles, CA 90290, USA

Mathematics, 2017, vol. 5, issue 2, 1-18

Abstract: 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.

Keywords: aperiodic Dirichlet lattice; icosahedral symmetry; Clifford spinors and Lie algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/5/2/29/pdf (application/pdf)
https://www.mdpi.com/2227-7390/5/2/29/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:5:y:2017:i:2:p:29-:d:99805

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().