In geometry, the kissing number is the maximum number of spheres of radius 1 that can simultaneously touch the unit sphere in n-dimensional Euclidean space. The kissing number problem seeks the kissing number as a function of n.
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
Kissing number | 2 | 6 | 12 | 24 | 40 | 72 | 126 | 240 |
Image | ||||||||
Isogonal polyhedron |
{6} |
t1{3,3} |
{3,4,3} |
r{3,3,4} |
122 |
231 |
421 | |
Isogonal tessellation | ||||||||
Isotopic polyhedron |
{3} |
Rhombic dodecahedron |
{3,4,3} | |||||
Isotopic tessellation |
The following table lists some known bounds on the kissing number in various dimensions. [1] The dimensions in which the kissing number is known are listed in boldface.
For 2..8, the best reflective tessellation geometries are given, and a few suboptimal ones.
{{
cite arXiv}}
: Unknown parameter |accessdate=
ignored (
help)
{{
cite journal}}
: Unknown parameter |ulr=
ignored (
help) English translation: V. A. Zinov'ev, T. Ericson (1999). "New Lower Bounds for Contact Numbers in Small Dimensions". Problems of Information Transmission. 35 (4): 287–294.
MR
1737742.
In geometry, the kissing number is the maximum number of spheres of radius 1 that can simultaneously touch the unit sphere in n-dimensional Euclidean space. The kissing number problem seeks the kissing number as a function of n.
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
Kissing number | 2 | 6 | 12 | 24 | 40 | 72 | 126 | 240 |
Image | ||||||||
Isogonal polyhedron |
{6} |
t1{3,3} |
{3,4,3} |
r{3,3,4} |
122 |
231 |
421 | |
Isogonal tessellation | ||||||||
Isotopic polyhedron |
{3} |
Rhombic dodecahedron |
{3,4,3} | |||||
Isotopic tessellation |
The following table lists some known bounds on the kissing number in various dimensions. [1] The dimensions in which the kissing number is known are listed in boldface.
For 2..8, the best reflective tessellation geometries are given, and a few suboptimal ones.
{{
cite arXiv}}
: Unknown parameter |accessdate=
ignored (
help)
{{
cite journal}}
: Unknown parameter |ulr=
ignored (
help) English translation: V. A. Zinov'ev, T. Ericson (1999). "New Lower Bounds for Contact Numbers in Small Dimensions". Problems of Information Transmission. 35 (4): 287–294.
MR
1737742.