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Rhombic Triacontahedral Graph


RhombicTriacontahedralGraph

The rhombic triacontahedral graph is Archimedean dual graph which is the skeleton of the rhombic triacontahedron, great rhombic triacontahedron, and small triambic icosahedron.

It is implemented in the Wolfram Language as GraphData["RhombicTriacontahedralGraph"].

RhombicTriacontahedralGraphMatrices

The plots above show the adjacency, incidence, and graph distance matrices for the deltoidal hexecontahedral graph.

The following table summarizes some properties of the graph.

propertyvalue
automorphism group order120
characteristic polynomialx^8(x^2-15)(x^2-3)^5(x^4-10x^2+5)^3
chromatic number2
chromatic polynomial?
claw-freeno
clique number2
determined by spectrum?
diameter6
distance-regular graphno
dual graph nameicosidodecahedral graph
edge chromatic number5
edge connectivity3
edge count60
Eulerianno
girth4
Hamiltonianno
Hamiltonian cycle count0
Hamiltonian path count0
integral graphno
independence number20
line graph?
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namesrhombic triacontahedron
radius6
regularno
square-freeno
traceableno
triangle-freeyes
vertex connectivity3
vertex count32

See also

Archimedean Dual Graph, Rhombic Triacontahedron

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Rhombic Triacontahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RhombicTriacontahedralGraph.html

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