Noncrystallographic Tail-triangle C-groups of Rank 4 and Interlacing Number 2

Authors

Mark L. Loyola, Ateneo de Manila UniversityFollow
Nonie Elvin S. Leyrita, Father Saturnino Urios University
Ma. Louise Antonette N. De las Peñas, Ateneo de Manila UniversityFollow

Document Type

Article

Publication Date

9-23-2024

Abstract

This work applies the modular reduction technique to the Coxeter group of rank 4 having a star diagram with labels 5, 3, and k = 3,4,5, or 6. As moduli, we use the primes in the quadratic integer ring Z[τ], where τ = (1+√5)/2, the golden ratio. We prove that each reduced group is a C-group, regardless of the prime used in the reduction. We also classify each reduced group as a reflection group over a finite field, whenever applicable.

Recommended Citation

Loyola, Mark L.; Leyrita, Nonie Elvin S.; and De las Peñas, Ma. Louise Antonette N., (2024). Noncrystallographic Tail-triangle C-groups of Rank 4 and Interlacing Number 2. Archīum.ATENEO.
https://archium.ateneo.edu/mathematics-faculty-pubs/306