In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral (and therefore by necessity also 3-vertex-connected planar graphs), and also Hamiltonian graphs. [1]
Along with the 13, the set of infinite prism graphs and antiprism graphs can also be considered Archimedean graphs. [2]
Name | Graph | Degree | Edges | Vertices | Order |
---|---|---|---|---|---|
truncated tetrahedral graph |
![]() |
3 | 18 | 12 | 24 |
cuboctahedral graph |
![]() |
4 | 24 | 12 | 48 |
truncated cubical graph |
![]() |
3 | 36 | 24 | 48 |
truncated octahedral graph |
![]() |
3 | 36 | 24 | 48 |
rhombicuboctahedral graph |
![]() |
4 | 48 | 24 | 48 |
truncated cuboctahedral graph (great rhombicuboctahedron) |
![]() |
3 | 72 | 48 | 48 |
snub cubical graph |
![]() |
5 | 60 | 24 | 24 |
icosidodecahedral graph |
![]() |
4 | 60 | 30 | 120 |
truncated dodecahedral graph |
![]() |
3 | 90 | 60 | 120 |
truncated icosahedral graph |
![]() |
3 | 90 | 60 | 120 |
rhombicosidodecahedral graph |
![]() |
4 | 120 | 60 | 120 |
truncated icosidodecahedral graph (great rhombicosidodecahedron) |
![]() |
3 | 180 | 120 | 120 |
snub dodecahedral graph |
![]() |
5 | 150 | 60 | 60 |
In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral (and therefore by necessity also 3-vertex-connected planar graphs), and also Hamiltonian graphs. [1]
Along with the 13, the set of infinite prism graphs and antiprism graphs can also be considered Archimedean graphs. [2]
Name | Graph | Degree | Edges | Vertices | Order |
---|---|---|---|---|---|
truncated tetrahedral graph |
![]() |
3 | 18 | 12 | 24 |
cuboctahedral graph |
![]() |
4 | 24 | 12 | 48 |
truncated cubical graph |
![]() |
3 | 36 | 24 | 48 |
truncated octahedral graph |
![]() |
3 | 36 | 24 | 48 |
rhombicuboctahedral graph |
![]() |
4 | 48 | 24 | 48 |
truncated cuboctahedral graph (great rhombicuboctahedron) |
![]() |
3 | 72 | 48 | 48 |
snub cubical graph |
![]() |
5 | 60 | 24 | 24 |
icosidodecahedral graph |
![]() |
4 | 60 | 30 | 120 |
truncated dodecahedral graph |
![]() |
3 | 90 | 60 | 120 |
truncated icosahedral graph |
![]() |
3 | 90 | 60 | 120 |
rhombicosidodecahedral graph |
![]() |
4 | 120 | 60 | 120 |
truncated icosidodecahedral graph (great rhombicosidodecahedron) |
![]() |
3 | 180 | 120 | 120 |
snub dodecahedral graph |
![]() |
5 | 150 | 60 | 60 |