Hyperbolic space
![A perspective projection of a dodecahedral tessellation in H3.Four dodecahedra meet at each edge, and eight meet at each vertex, like the cubes of a cubic tessellation in E3](/Images/godic/202501/19/Hyperbolic_orthogonal_dodecahedral_honeycomb5636.png")
In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature. It is hyperbolic geometry in more than 2 dimensions, and is distinguished from Euclidean spaces with zero curvature that define the Euclidean geometry, and elliptic geometry that have a constant positive curvature.