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    Platonic Graph

    Graphs with available data

    tetrahedral graph | octahedral graph | cubical graph | icosahedral graph | dodecahedral graph

    Images

    Basic properties

    | vertex count | edge count | connected component count tetrahedral graph | 4 | 6 | 1 octahedral graph | 6 | 12 | 1 cubical graph | 8 | 12 | 1 icosahedral graph | 12 | 30 | 1 dodecahedral graph | 20 | 30 | 1

    Common graph features

    apex | arc-transitive | biconnected | bridgeless | class 1 | completely regular | conformally rigid | connected | cyclic | determined by spectrum | distance-regular | distance-transitive | edge-transitive | fully reconstructible in C^1 | graceful | Hamilton-decomposable | Hamiltonian | LCF | linklessly embeddable | local | map | nonempty | perfect matching | planar | Platonic | polyhedral | projective planar | quadratically embeddable | regular | simple | symmetric | traceable | uniform skeleton | uniquely embeddable | vertex-transitive

    Complement graph

    | complement graph name tetrahedral graph | 4-empty graph octahedral graph | 3-ladder rung graph cubical graph | (2, 4)-rook graph icosahedral graph | 12-vertex transitive graph 40 dodecahedral graph | (20, 81)-noncayley transitive graph

    Dual graph

    | dual graph name tetrahedral graph | tetrahedral graph octahedral graph | cubical graph cubical graph | octahedral graph icosahedral graph | dodecahedral graph dodecahedral graph | icosahedral graph

    Line graph

    | line graph name tetrahedral graph | octahedral graph octahedral graph | octahedral line graph cubical graph | cuboctahedral graph icosahedral graph | line graph of the icosahedral graph dodecahedral graph | icosidodecahedral graph