  There is no settled universal 3D representation for geometry with many
alternatives such as point clouds, meshes, implicit functions, and voxels to
name a few. In this work, we present a new, compelling alternative for
representing shapes using a sequence of cross-sectional closed loops. The loops
across all planes form an organizational hierarchy which we leverage for
autoregressive shape synthesis and editing. Loops are a non-local description
of the underlying shape, as simple loop manipulations (such as shifts) result
in significant structural changes to the geometry. This is in contrast to
manipulating local primitives such as points in a point cloud or a triangle in
a triangle mesh. We further demonstrate that loops are intuitive and natural
primitive for analyzing and editing shapes, both computationally and for users.
