A new addition to the zoo of isolated symplectic singularities

We give details of a new isolated symplectic singularity found in an affine chart in a crepant partial resolution of ${\mathbb{C}}^4\mathrm{/}{G}_5$, which is 4-dimensional, isolated, and locally simply-connected. We distinguish the new singularity among all known such by the fact that the projective tangent cone at the singularity is non-reduced. We also find all 12 of its $\mathbb{Q}$-factorial terminalisations, in the process finding 24 for the quotient singularity ${\mathbb{C}}^4\mathrm{/}{G}_5$.