# 8-cell

## English

A Schlegel diagram of an 8-cell
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8 +‎ cell

### Noun

8-cell (plural 8-cells)

1. (geometry) A four-dimensional polytope, analogous to a cube, whose eight bounding facets are cubes.
• 1988, Klaus Mainzer, Symmetries of Nature: A Handbook for Philosophy of Nature and Science, 1996, page 159,
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.
• 1996, John Milnor, Growing Up in the Old Fine Hall, Hugo Rossi (editor), Prospects in Mathematics: Invited Talks on the Occasion of the 250th Anniversary of Princeton University, page 6,
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.
• 1997, J. François Gabriel (editor), Beyond the Cube: The Architecture of Space Frames and Polyhedra[1], page 412:
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).