(2,3,7)-triangle group

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Definition

The $(7,3,2)$-triangle group or $(2,3,7)$-triangle group is defined as the triangle group with parameters $(7,3,2)$. Equivalently, it is defined as:

$⟨s_1,s_2,s_3\mid s_1^2=s_2^2=s_3^2=(s_1{s}_2{)}^7=(s_2{s}_3{)}^3=(s_3{s}_1{)}^2=e⟩$.

Here, $e$ is the identity element.

The term $(7,3,2)$-triangle group or $(2,3,7)$-triangle group is also used for the subgroup of index two in this group, which we refer to (7,3,2)-von Dyck group.