In this question, the space $E$ has dimension $n = 2$. For every root system $\mathcal { R }$ of $E$, we set $$\theta _ { \mathcal { R } } = \min \left\{ \theta _ { \alpha , \beta } \mid ( \alpha , \beta ) \in \mathcal { R } ^ { 2 } , \alpha \neq \beta \text { and } \alpha \neq - \beta \right\}$$ For each value of $k \in \{ 2,3,4,6 \}$, draw graphically a root system $\mathcal { R } _ { k }$ such that $\theta _ { \mathcal { R } _ { k } } = \pi / k$. It is not necessary to justify that the figures drawn represent root systems. What is the cardinality of $\mathcal { R } _ { k }$? No justification is required.
In this question, the space $E$ has dimension $n = 2$. For every root system $\mathcal { R }$ of $E$, we set
$$\theta _ { \mathcal { R } } = \min \left\{ \theta _ { \alpha , \beta } \mid ( \alpha , \beta ) \in \mathcal { R } ^ { 2 } , \alpha \neq \beta \text { and } \alpha \neq - \beta \right\}$$
For each value of $k \in \{ 2,3,4,6 \}$, draw graphically a root system $\mathcal { R } _ { k }$ such that $\theta _ { \mathcal { R } _ { k } } = \pi / k$. It is not necessary to justify that the figures drawn represent root systems. What is the cardinality of $\mathcal { R } _ { k }$? No justification is required.