8-cell

plural 8-cells

1. geometryA four-dimensional polytope, analogous to a cube, whose eight bounding facets are cubes; a tesseract.

   Similarly in dimension eight there is the quaternionic projective plane which we can think of as a 4-sphere with an 8-cell attached, and in dimension sixteen there is a Cayley projective plane which has similar properties.

   1996, John Milnor, “Growing Up in the Old Fine Hall”, in Hugo Rossi, editor, Prospects in Mathematics: Invited Talks on the Occasion of the 250th Anniversary of Princeton University, page 6

   2 more examples

   According to this table the tetrahedron corresponds to the 5-cell, the cube to the 8-cell ("hypercube"), the octahedron to the 16-cell, the dodecahedron to the 120-cell and the icosahedron to the 600-cell. The 24-cell is an additional body in four-dimensional space which is dual to itself.

   1988, Klaus Mainzer, Symmetries of Nature: A Handbook for Philosophy of Nature and Science, published 1996, page 159

   Of these nine, five are finite structures in Euclidean space and include the simplex, {3,3,3} (or 5-cell), the four-dimensional cube {4,3,3} (or 8-cell) and its dual {3,3,4} (or 16-cell), and the 120-cell {5,3,3} and its dual {3,3,5} (or 600-cell).

   1997, J. François Gabriel, editor, Beyond the Cube: The Architecture of Space Frames and Polyhedra, page 412

   Synonyms: 4-cube, hypercube, cubic prism, octachoron, octahedroid, tesseract