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Download as PDF; Printable version; ... It can be seen as regular map {8,3} 2,0 on a hyperbolic plane with 6 colored ... Platonic solid; Platonic graph; References
The polyhedral graph formed as the Schlegel diagram of a regular dodecahedron. In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron. Alternatively, in purely graph-theoretic terms, the polyhedral graphs are the 3-vertex-connected, planar graphs.
Download as PDF; Printable version; In other projects ... 2, 3, 4} represent the vertices ... It is one of 5 Platonic graphs, ...
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 .
v3.3.3.3.3 The above shapes may also be realized as slices orthogonal to the long diagonal of a tesseract . If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r , 3 / 8 , 1 / 2 , 5 / 8 , and s , where r is any number in the range 0 < r ≤ 1 / 4 , and s ...
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]
Hamiltonian platonic graphs: Image title: Orthographic projections and planar graphs of Hamiltonian cycles of the vertices of the five Platonic solids by CMG Lee. Only the octahedron has an Eulerian path, made by extending the Hamiltonian path with the dotted path. Width: 100%: Height: 100%
The Platonic solids known to antiquity are the only integer solutions for m ≥ 3 and n ≥ 3. The restriction m ≥ 3 enforces that the polygonal faces must have at least three sides. When considering polyhedra as a spherical tiling , this restriction may be relaxed, since digons (2-gons) can be represented as spherical lunes, having non-zero ...