For questions related to hypercone (or spherical cone). It's a $4$D Euclidean space represented by the equation $x^{2}+y^{2}+z^{2}-w^{2}=0$.
In geometry, a hypercone (or spherical cone) is the figure in the $4$-dimensional Euclidean space represented by the equation $x^{2}+y^{2}+z^{2}-w^{2}=0$.
It is a quadric surface, and is one of the possible $3$-manifolds which are $4$-dimensional equivalents of the conical surface in $3$ dimensions. It is also named "spherical cone" because its intersections with hyperplanes perpendicular to the $w$-axis are spheres. A four-dimensional right hypercone can be thought of as a sphere which expands with time, starting its expansion from a single point source, such that the center of the expanding sphere remains fixed. An oblique hypercone would be a sphere which expands with time, again starting its expansion from a point source, but such that the center of the expanding sphere moves with a uniform velocity.
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