Search results
Results from the WOW.Com Content Network
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.
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]
Download as PDF; Printable version; In other projects ... The 5 Platonic solids are called a tetrahedron, ... {3} +2{6} Heptagonal antiprism ...
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 ...
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%
It can also be found in nature and supramolecules, as well as the shape of the universe. The skeleton of a regular dodecahedron can be represented as the graph called the dodecahedral graph, a Platonic graph. Its property of the Hamiltonian, a path visits all of its vertices exactly once, can be found in a toy called icosian game.
Download as PDF; Printable version; ... 3 axes, 2 per axis, together 6; equivalently, ... It is one of 5 Platonic graphs, ...
For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 3 6 ; 3 6 (both of different transitivity class), or (3 6 ) 2 , tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided ...