2025年1月20日 · Given four colors, there are two distinct ways to color a tetrahedron (Ball and Coxeter 1987, p. 238) and four ways to color a dodecahedron, consisting of two …

Dedecahedral graph is Schlegel diagram of dodecahedron. It is planar  graph with chromatic number 4. The problem of coloring a graph arises in many practical areas such as pattern …

If a dodecahedron is colored with four colors so that no two adjacent faces have the same color, there is only one coloring, up to a permutation of the colors or a rotation.

By the Four color theorem , the faces of a dodecahedron are four-colorable; that is, one can pick a color among four for each face in such a way that no two adjacent faces share the same color. …

The purpose of this note is to show that there is one and only one coloring of the sides of a dodecahedron with four colors, under the condition that no two adjacent sides share the same …

2015年5月10日 · You need to work out what the group of rotations of a dodecahedron is (assuming you are not considering reflections), and find the number of colourings which are …

2015年12月23日 · I have an origami model of a dodecahedron I am assembling. There are 30 edges with 3 colors of 10 each. I could use a diagram that gives a possible 3 color edge …

2021年5月31日 · What are the chromatic numbers of the edge graphs of the platonic solids? For the cube graph, its chromatic number is 2, because it is a bipartite graph. The tetrahedron is …

1999年5月25日 · Given two colors, there is a single way to color an Octahedron. Given three colors, there is one way to color a Cube and 144 ways to color an Icosahedron. Given four …

Coloring the edges of a dodecahedron or icosahedron is equivalent to coloring the faces of a rhombic triacontahedron. This follows from the way a dodecahedron can be inscribed in a …