Meaning of 8-cell | Babel Free

Definitions

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

Equivalents

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.”

“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.”

“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).”

CEFR level