Simple Reflection s[1]:
{
alpha[1]: -alpha[1],
alpha[2]: alpha[2],
alpha[3]: alpha[1] + alpha[3],
alpha[4]: alpha[4],
alpha[5]: alpha[5],
alpha[6]: alpha[6],
}

Simple Reflection s[2]:
{
alpha[1]: alpha[1],
alpha[2]: -alpha[2],
alpha[3]: alpha[3],
alpha[4]: alpha[2] + alpha[4],
alpha[5]: alpha[5],
alpha[6]: alpha[6],
}

Simple Reflection s[3]:
{
alpha[1]: alpha[1] + alpha[3],
alpha[2]: alpha[2],
alpha[3]: -alpha[3],
alpha[4]: alpha[3] + alpha[4],
alpha[5]: alpha[5],
alpha[6]: alpha[6],
}

Simple Reflection s[4]:
{
alpha[1]: alpha[1],
alpha[2]: alpha[2] + alpha[4],
alpha[3]: alpha[3] + alpha[4],
alpha[4]: -alpha[4],
alpha[5]: alpha[4] + alpha[5],
alpha[6]: alpha[6],
}

Simple Reflection s[5]:
{
alpha[1]: alpha[1],
alpha[2]: alpha[2],
alpha[3]: alpha[3],
alpha[4]: alpha[4] + alpha[5],
alpha[5]: -alpha[5],
alpha[6]: alpha[5] + alpha[6],
}

Simple Reflection s[6]:
{
alpha[1]: alpha[1],
alpha[2]: alpha[2],
alpha[3]: alpha[3],
alpha[4]: alpha[4],
alpha[5]: alpha[5] + alpha[6],
alpha[6]: -alpha[6],
}