6D hypercube, 6-cube or Hexeract
This screen recording showcases an upcoming interactive macOS app that visualises 3D projections of hypercubes ranging from 4 to 6 dimensions (with more to be added in the future).
Wikipedia about 6-cube:
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
It has Schläfli symbol {4,34}, being composed of 3 5-cubes around each 4-face. It can be called a hexeract, a portmanteau of tesseract (the 4-cube) with hex for six (dimensions) in Greek. It can also be called a regular dodeca-6-tope or dodecapeton, being a 6-dimensional polytope constructed from 12 regular facets.