# Is the octahedron a planar graph?

## Is the octahedron a planar graph?

The cubical graph is an octahedral graph….Octahedral Graph.

property | value |
---|---|

planar | yes |

polyhedral graph | yes |

polyhedron embedding names | octahedron, tetrahemihexahedron |

radius | 2 |

### What is a Plato in a graph?

In the mathematical field of graph theory, a Platonic graph is a graph that has one of the Platonic solids as its skeleton.

**What is a octahedron used for?**

The shape looks like two pyramids stacked base to base. One use for regular octahedrons is in the creation of eight sided dice.

**Is octahedral 2d or 3d?**

An octahedron is the three-dimensional case of the more general concept of a cross polytope.

## What is the net of a octahedron?

There are 11 distinct nets for an octahedron, the same number of nets as for a cube, see Figure 17. All nets have eight triangular faces.

### What is a tripartite graph?

In other words, it is a tripartite graph (i.e., a set of graph vertices decomposed into three disjoint sets such that no two graph vertices within the same set are adjacent) such that every vertex of each set graph vertices is adjacent to every vertex in the other two sets.

**Are dodecahedron graphs planar?**

The line graph of the dodecahedral graph is the icosidodecahedral graph….Dodecahedral Graph.

property | value |
---|---|

planar | yes |

polyhedral graph | yes |

polyhedron embedding names | dodecahedron, great stellated dodecahedron |

radius | 5 |

**What is octahedral shape?**

In chemistry, octahedral molecular geometry describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron has eight faces, hence the prefix octa.

## What is a K3 3 graph?

K3,3: K3,3 has 6 vertices and 9 edges, and so we cannot apply Lemma 2. But notice that it is bipartite, and thus it has no cycles of length 3. We may apply Lemma 4 with g = 4, and this implies that K3,3 is not planar. • Any graph containing a nonplanar graph as a subgraph is nonplanar.