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Pentakis Dodecahedral Graph


PentakisDodecahedralGraph

The pentakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as GraphData["PentakisDodecahedralGraph"].

PentakisDodecahedralGraphMatrices

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^4(x+2)^4(x^2-3x-15)(x^2-x-3)^5(x^4-15x^2-20x+5)^3
chromatic number4
chromatic polynomial?
claw-freeno
clique number3
determined by spectrum?
diameter5
distance-regular graphno
dual graph nametruncated icosahedral graph
edge chromatic number6
edge connectivity5
edge count90
Eulerianno
girth3
Hamiltonianyes
Hamiltonian cycle count?
Hamiltonian path count?
integral graphno
independence number12
line graph?
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namespentakis dodecahedron, small stellated dodecahedron
radius5
regularno
square-freeno
traceableyes
triangle-freeno
vertex connectivity5
vertex count32

See also

Archimedean Dual Graph, Pentakis Dodecahedron

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Pentakis Dodecahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PentakisDodecahedralGraph.html

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