In the
mathematical field of
graph theory, a Platonic graph is a
graph that has one of the
Platonic solids as its skeleton. There are 5 Platonic graphs, and all of them are
regular
The term regular can mean normal or in accordance with rules. It may refer to:
People
* Moses Regular (born 1971), America football player
Arts, entertainment, and media Music
* "Regular" (Badfinger song)
* Regular tunings of stringed instrum ...
,
polyhedral (and therefore by necessity also
3-vertex-connected,
vertex-transitive,
edge-transitive and
planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross ...
s), and also
Hamiltonian graphs.
[Read, R. C. and Wilson, R. J. ''An Atlas of Graphs'', Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 ''special graphs'' pp. 261, 266.]
*
Tetrahedral graph – 4 vertices, 6 edges
*
Octahedral graph – 6 vertices, 12 edges
*
Cubical graph – 8 vertices, 12 edges
*
Icosahedral graph – 12 vertices, 30 edges
*
Dodecahedral graph – 20 vertices, 30 edges
See also
*
Regular map (graph theory)
*
Archimedean graph
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-vert ...
*
Wheel graph
References
External links
*
{{combin-stub
Graph families
Regular graphs
Planar graphs