Definition of Horosphere. Meaning of Horosphere. Synonyms of Horosphere

- In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a...
- the Böröczky bound is approximately 85.327613%, and is realized by the horosphere ****ng of the order-6 tetrahedral honeycomb with Schläfli symbol {3,3...
- number of faces. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at...
- {\displaystyle {\overline {\mathbf {p} \mathbf {q} }}} . Let H be some horosphere such that points of the form ( w , x , 0 , … , 0 ) {\displaystyle (w,x...
- away from each other and stay at an infinite distance off its centre. A horosphere is the 3-dimensional version of a horocycle. In Euclidean space, all curves...
- limit at a single ideal point. These Euclidean tilings are inscribed in a horosphere just as polyhedra are inscribed in a sphere (which contains zero ideal...
- number of faces. Each cell is a hexagonal tiling whose vertices lie on a horosphere: a flat plane in hyperbolic space that approaches a single ideal point...
- number of faces. Each cell is a hexagonal tiling whose vertices lie on a horosphere: a flat plane in hyperbolic space that approaches a single ideal point...
- if Euclidean geometry was. (The reverse implication follows from the horosphere model of Euclidean geometry.) In the hyperbolic model, within a two-dimensional...
- faces. Each cell consists of a hexagonal tiling whose vertices lie on a horosphere, a flat plane in hyperbolic space that approaches a single ideal point...