Abstract: This is a report on ongoing joint work with Gustavo Jasso. Let D be the triangulated category associated to a spherical object of dimension m greater than or equal to 2. By work of Jørgensen, D is an m-Calabi-Yau triangulated category with almost split triangles classically generated by a spherical object. Moreover, its Auslander-Reiten quiver has m-1 connected components of type ZA-infinity. Building upon work of Amiot, Guo, Keller, and Oppermann-Thomas, for each positive integer d we construct an md-Calabi-Yau weakly (d+2)-angulated category with almost split (d+2)-angles, classically enerated by a spherical object. Moreover, its higher Auslander-Reiten quiver has m-1 connected components of higher mesh type A-infty. For m=2, our construction is analogous to the cluster category of type A-infinity introduced by Holm-Jørgensen.