Geometry · combinatorics · topology
A hands-on guide to Goodwillie polytopes.
Rotate, separate, and inspect the geometry behind a family of polytopes arising in the study of free loop spaces.
Explore the guidesInteractive chapters
Begin with the shape.
01Inflating a cubeFollow the geometric idea that opens a cube into G₃.02Low dimensionsCompare G₁, G₂, and G₃ at a glance.03Prismatic decompositionPull apart the four maximal cells of G₃.04Self-dualityPair every vertex with its corresponding facet.05Goodwillie to freehedronCollapse G₃ onto F₃ through the deformation retraction—and reverse it.06Boolean navigatorPredict cell intersections from subsets of {2,3}.07Incidence matrixRead self-duality as a symmetric 12 × 12 matrix.08Epsilon laboratoryMove ε from 0 to 5 and watch the hull cross exact events.09Canonical face builderTurn an R/M/Z/N partition into a product face.10Regular liftingSee how lower support functions recover the prism cells.