  We construct a new infinite family of 4-dimensional isolated symplectic
singularities with trivial local fundamental group, answering a question of
Beauville raised in 2000. Three constructions are presented for this family:
(1) as singularities in blowups of the quotient of $\mathbb{C}^4$ by the
dihedral group of order $2d$, (2) as singular points of Calogero-Moser spaces
associated with dihedral groups of order $2d$ at equal parameters, (3) as
singularities of a certain Slodowy slice in the $d$-fold cover of the nilpotent
cone in ${\mathfrak{sl}}_d$.
