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Tetrakis Hexahedral Graph


TetrakisHexahedralGraph

The tetrakis hexahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as GraphData["TetrakisHexahedralGraph"].

TetrakisHexahedralGraphMatrices

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 order48
characteristic polynomialx^2(x+1)^3(x+3)(x^2-3x-12)(x^2-x-4)^3
chromatic number3
chromatic polynomial(x-2)(x-1)x(x^(11)-33x^(10)+505x^9-4737x^8+30316x^7-139236x^6+468913x^5-1158486x^4+2056136x^3-2491774x^2+1849898x-634928)
claw-freeno
clique number3
determined by spectrum?
diameter3
distance-regular graphno
dual graph nametruncated octahedral graph
edge chromatic number6
edge connectivity4
edge count36
Eulerianyes
girth3
Hamiltonianyes
Hamiltonian cycle count3408
Hamiltonian path count?
integral graphno
independence number6
line graph?
line graph name?
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namestetrakis hexahedron
radius3
regularno
square-freeno
traceableyes
triangle-freeno
vertex connectivity4
vertex count14

See also

Archimedean Dual Graph, Disdyakis Triacontahedron

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Tetrakis Hexahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TetrakisHexahedralGraph.html

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