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2. mathworld.wolfram.com · PlatonicGraphPlatonic Graph -- from Wolfram MathWorld

   mathworld.wolfram.com · PlatonicGraph

   

   Aug 22, 2024 · Platonic Graph. A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, and icosahedral graph, are illustrated above. They are special cases of Schlegel graphs.

   • Graceful

     A graceful graph is a graph that can be gracefully labeled....

   • Octahedral Graph

     "The" octahedral graph is the 6-node 12-edge Platonic graph...

   • Icosahedral Graph

     The icosahedral graph is the Platonic graph whose nodes have...

   • Cubical Graph

     The cubical graph is the Platonic graph corresponding to the...

   • Cubic

     Cubic graphs, also called trivalent graphs, are graphs all...

   • Platonic Solid

     The Platonic solids, also called the regular solids or...

   • Dodecahedral Graph

     The dodecahedral graph is the Platonic graph corresponding...

   • Schlegel Graph

     References Gardner, M. Wheels, Life, and Other Mathematical...

3. People also ask

   What are the 5 Platonic graphs?

   • The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, and icosahedral graph, are illustrated above. They are special cases of Schlegel graphs . Platonic graphs are graceful (Gardner 1983, pp. 158 and 163-164). The following table summarizes the Platonic graphs and some of their properties.

   Platonic Graph -- from Wolfram MathWorld

   mathworld.wolfram.com/PlatonicGraph.html

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   What are Platonic graphs?

   • The graphs of the Platonic solids have been called Platonic graphs. As well as having all the other properties of polyhedral graphs, these are symmetric graphs, and all of them have Hamiltonian cycles. There are five of these graphs:

   Polyhedral graph - Wikipedia

   en.wikipedia.org/wiki/Polyhedral_graph

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   How many Platonic solids are there in a planar graph?

   • After first defining planar graphs, we will prove that Euler’s characteristic holds true for any of them. We will then define Platonic solids, and then using Euler’s formula, prove there exists only five.

   Euler's formula and Platonic solids - University of Washington

   sites.math.washington.edu/~julia/teaching/445_Spring2013/Paper_Euler.pdf

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   Are Platonic graphs graceful?

   • Platonic graphs are graceful (Gardner 1983, pp. 158 and 163-164). The following table summarizes the Platonic graphs and some of their properties. Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 234, 1976. Gardner, M. "Golomb's Graceful Graphs."

   Platonic Graph -- from Wolfram MathWorld

   mathworld.wolfram.com/PlatonicGraph.html

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4. en.wikipedia.org · wiki · Polyhedral_graphPolyhedral graph - Wikipedia

   en.wikipedia.org · wiki · Polyhedral_graph

   

   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.

5. faculty.etsu.edu · gardnerr · 5025Foundations and Structure of Mathematics 1 "The Platonic ...

   faculty.etsu.edu · gardnerr · 5025

   

   A graph is a (finite) collection of dots called vertices and a collection of line segments, called edges, which join some of the vertices. The only properties of a graph are: the number of vertices, the number of edges, and the connectivity of vertices by edges. For a given graph, we can have several drawings:

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6. Searches related to platonic graph

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7. mathworld.wolfram.com · DodecahedralGraphDodecahedral Graph -- from Wolfram MathWorld

   mathworld.wolfram.com · DodecahedralGraph

   

   The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings.

8. www2.math.upenn.edu · ~mlazar · math1705.4 Polyhedral Graphs and the Platonic Solids

   www2.math.upenn.edu · ~mlazar · math170

   

   Learn how to construct polyhedral graphs from regular polyhedra and how to use Euler's formula to count their faces, edges, and vertices. Explore the five Platonic solids and their properties as three-dimensional analogues of regular polygons.

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9. sites.math.washington.edu · ~julia · teachingEuler's formula and Platonic solids - University of Washington

   sites.math.washington.edu · ~julia · teaching

   

   Jun 3, 2013 · In this paper, we will present the concepts of planar graphs, Euler’s characteristic formula, and Platonic solids and show their relationships to one another. After first defining planar graphs, we will prove that Euler’s characteristic holds true for any of them. We will then define Platonic solids, and then using Euler’s

10. polyhedra.tessera.liPolyhedra Viewer

    polyhedra.tessera.li

    

    The uniform polyhedra are the Platonic solids, the Archimedean solids, and the infinite set of prisms and antiprisms.