 DodecahedronGraph - Maple Help

GraphTheory[SpecialGraphs]

 TetrahedronGraph
 construct tetrahedron graph
 OctahedronGraph
 construct octahedron graph
 DodecahedronGraph
 construct dodecahedron graph
 IcosahedronGraph
 construct icosahedron graph Calling Sequence TetrahedronGraph() TetrahedronGraph(V1) OctahedronGraph() OctahedronGraph(V2) DodecahedronGraph() DodecahedronGraph(V3) IcosahedronGraph() IcosahedronGraph(V4) Parameters

 V1 - (optional) set or list of 4 vertex labels V2 - (optional) set or list of 6 vertex labels V3 - (optional) set or list of 20 vertex labels V4 - (optional) set or list of 12 vertex labels Description

 • The TetrahedronGraph command creates the tetrahedron graph (the complete graph) on 4 vertices. As an option, you may input the labels of the vertices as a set or list of size 4.
 • The OctahedronGraph command creates the octahedron graph on 6 vertices. As an option, you may input the labels of the vertices as a set or list of size 6.
 • The DodecahedronGraph command creates the dodecahedron graph on 20 vertices. A dodecahedron is a 3-regular and 12-faced planar graph. As an option, you may input the labels of the vertices as a set or list of size 20.
 • The IcosahedronGraph command creates the icosahedron graph on 12 vertices. An icosahedron is a 5-regular and 20-faced planar graph. As an option, you may input the labels of the vertices as a set or list of size 12. Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $T≔\mathrm{TetrahedronGraph}\left(\right)$
 ${T}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 4 vertices and 6 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(T\right)$ > $G≔\mathrm{OctahedronGraph}\left(\right)$
 ${G}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 6 vertices and 12 edge\left(s\right)}}$ (2)
 > $\mathrm{IsPlanar}\left(G\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{DrawGraph}\left(G\right)$ > $H≔\mathrm{DodecahedronGraph}\left(\right)$
 ${H}{≔}{\mathrm{Graph 3: an undirected unweighted graph with 20 vertices and 30 edge\left(s\right)}}$ (4)
 > $\mathrm{Neighborhood}\left(H,19\right)$
 $\left[{14}{,}{18}{,}{20}\right]$ (5)
 > $\mathrm{IsPlanar}\left(H,'F'\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{nops}\left(F\right)$
 ${12}$ (7)
 > $\mathrm{DrawGraph}\left(H\right)$ > $K≔\mathrm{IcosahedronGraph}\left(\right)$
 ${K}{≔}{\mathrm{Graph 4: an undirected unweighted graph with 12 vertices and 30 edge\left(s\right)}}$ (8)
 > $\mathrm{IsPlanar}\left(K,'F'\right)$
 ${\mathrm{true}}$ (9)
 > $\mathrm{map}\left(\mathrm{nops},F\right)$
 $\left[{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}\right]$ (10)
 > $\mathrm{DrawGraph}\left(K\right)$ 