For every tetrahedron, there exists one of theseobjects such that all the tetrahedron's vertices lie on its surface, and this object names a set of coordinatesthat includes the quantities rho, phi and theta.
John Milnor was the first to show that there exists a smooth manifold which is homeomorphic butnot diffeomorphic to an n-dimensional version of this construct. Casson names an integer-valuedinvariant of one type of this object. John Leech created a lattice that gives the tighest packing of theseobjects in 24 dimensions, and the (*) kissing number problem involves how many of these objects in ndimensions can touch an equivalent object without any intersections. Kepler conjectured that the densestpossible packing of these objects was approximately 74%. For every tetrahedron, there exists one of theseobjects such that all the tetrahedron's vertices lie on its surface, and this object names a set of coordinatesthat includes the quantities rho, phi and theta. For 10 points, name this object whose two dimensionalversion is a circle.
John Milnor was the first to show that there exists a smooth manifold which is homeomorphic butnot diffeomorphic to an n-dimensional version of this construct.
hypersphere