We investigate toric varieties defined by arrangements of hyperplanes and call them strongly symmetric. The smoothness of such a toric variety translates to the fact that the arrangement is crystallographic. As a result, we obtain a complete classification of this class of toric varieties. Further, we show that these varieties are projective and describe associated toric arrangements in these varieties.
"Strongly symmetric smooth toric varieties." Kyoto J. Math. 52 (3) 597 - 620, Fall 2012. https://doi.org/10.1215/21562261-1625208