Archimedean graph

{{Short description|Graph with an Archimedean solid as its skeleton}}

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.An Atlas of Graphs, p. 267-270

Along with the 13, the infinite sets of prism graphs and antiprism graphs can also be considered Archimedean graphs.An Atlas of Graphs, p. 261

class="wikitable sortable" style="text-align:center" |+ Graph elements
Name !Graph ! Degree ! Edges ! Vertices ! Automorphisms
truncated tetrahedral graph	60px	3	18	12	24
cuboctahedral graph	60px	4	24	12	48
truncated cubical graph	60px	3	36	24	48
truncated octahedral graph	60px	3	36	24	48
rhombicuboctahedral graph	60px	4	48	24	48
truncated cuboctahedral graph (great rhombicuboctahedron)	60px	3	72	48	48
snub cubical graph	60px	5	60	24	24
icosidodecahedral graph	60px	4	60	30	120
truncated dodecahedral graph	60px	3	90	60	120
truncated icosahedral graph	60px	3	90	60	120
rhombicosidodecahedral graph	60px	4	120	60	120
truncated icosidodecahedral graph (great rhombicosidodecahedron)	60px	3	180	120	120
snub dodecahedral graph	60px	5	150	60	60