Orthographic projections and Schlegel diagrams with Hamiltonian cycles of the vertices of the five platonic solids – only the octahedron has an Eulerian path or cycle, by extending its path with the dotted one
platonic, graph, mathematical, field, graph, theory, graph, that, platonic, solids, skeleton, there, them, regular, polyhedral, therefore, necessity, also, vertex, connected, vertex, transitive, edge, transitive, planar, graphs, also, hamiltonian, graphs, tetr. 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 polyhedral and therefore by necessity also 3 vertex connected vertex transitive edge transitive and planar graphs and also Hamiltonian graphs 1 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 edgesOrthographic projections and Schlegel diagrams with Hamiltonian cycles of the vertices of the five platonic solids only the octahedron has an Eulerian path or cycle by extending its path with the dotted one vteThe platonic graphs can be seen as Schlegel diagrams of the platonic solids excluding the square pyramid also shown here Orthogonal projections of platonic solidsSee also EditRegular map graph theory Archimedean graph Wheel graphReferences Edit 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 External links EditWeisstein Eric W Platonic graph MathWorld nbsp This graph theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Platonic graph amp oldid 1169852277, wikipedia, wiki, book, books, library,
