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.