8-cell

Noun

8-cell (plural 8-cells)

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

   Synonyms:

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