This work applies the modular reduction technique to the Coxeter group of rank 4 having a star diagram with labels 5, 3, and $k = 3, 4, 5, \text{ or } 6$. As moduli, we use the primes in the quadratic integer ring $\mathbb{ Z}[\tau]$, where $\tau = \frac{ 1 + \sqrt{ 5}}{ 2}$, 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.
Categories: math.GR