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...

edges, and 12 vertices. It is an example of the Platonic solid and of the deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron...

a symmetric graph. Similarly to the Platonic graphs, the cycle graphs form the skeletons of the dihedra. Their duals are the dipole graphs, which form...

forms a graph with 8 vertices and 12 edges, called the cube graph. It is a special case of the hypercube graph. It is one of 5 Platonic graphs, each a...

of Hamiltonian paths (Rédei 1934) Every platonic solid, considered as a graph, is Hamiltonian The Cayley graph of a finite Coxeter group is Hamiltonian...

a graph. It is one of 5 Platonic graphs, each a skeleton of its Platonic solid. This graph can also be constructed as the generalized Petersen graph G(10...

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...

is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed...

graphs (such as the Petersen graph, the Heawood graph and the vertices and edges of the Platonic solids). The finite Cayley graphs (such as cube-connected...

lines. Topological graph theory Abstract polytope Planar graph Toroidal graph Graph embedding Regular tiling Platonic solid Platonic graph Nedela (2007) Coxeter...

duality to be recognized was the association of the Platonic solids into pairs of dual polyhedra. Graph duality is a topological generalization of the geometric...

Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Holt graph Horton...

Archimedean graphs. Platonic graph Wheel graph An Atlas of Graphs, p. 267-270 An Atlas of Graphs, p. 261 Read, R. C. and Wilson, R. J. An Atlas of Graphs, Oxford...

covering graph of D4. Similarly to the Platonic graphs, the dipole graphs form the skeletons of the hosohedra. Their duals, the cycle graphs, form the...

forms a graph, with 4 vertices, and 6 edges. It is a special case of the complete graph, K4, and wheel graph, W4. It is one of 5 Platonic graphs, each a...

the largest face that any of the five regular three-dimensional regular Platonic solid can have, as represented in the regular dodecahedron. For curves...

hexagons, and 12 regular decagons. It has the most edges and vertices of all Platonic and Archimedean solids, though the snub dodecahedron has more faces. Of...

In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than...

constructed from the Platonic solids by a process called stellation. Most stellations are not regular. The study of stellations of the Platonic solids was given...

theorems about them, including the classification of the Platonic solids. It was stated for Platonic solids in 1537 in an unpublished manuscript by Francesco...

The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each...

rhombicuboctahedral graph is the graph of vertices and edges of the rhombicuboctahedron. It has 24 vertices and 48 edges, and is a quartic Archimedean graph. Compound...

interpretation of quantum mechanics and the philosophical debate between Platonic realism and nominalism. Anathem is set on the fictional planet of Arbre...

symmetric vertices, which is divided into the Archimedean solids, the five Platonic solids (each with only one type of polygon face), and the two infinite...

Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to...

S2CID 85618870. Lanphier, D.; Rosenhouse, J. (2004). "Cheeger constants of Platonic graphs". Discrete Mathematics. 277 (1–3): 101–113. doi:10.1016/S0012-365X(03)00178-X...

McKay. The connection to Platonic solids is described in (Dickson 1959). The correspondence uses the construction of McKay graph. Note that the ADE correspondence...

isomorphic if their face lattices are isomorphic. The polytope graph (polytopal graph, graph of the polytope, 1-skeleton) is the set of vertices and edges...

study of the attraction between people which leads to the development of platonic or romantic relationships. It is distinct from perceptions such as physical...

this, they are not necessarily topologically equivalent to the sphere as Platonic solids are, and in particular the Euler relation χ = V − E + F = 2   {\displaystyle...