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In the mathematical field of graph theory, an antiprism graph is a graph that has one of the antiprisms as its skeleton. An n-sided antiprism has 2n vertices and 4n edges. They are regular, polyhedral (and therefore by necessity also 3-vertex-connected, vertex-transitive, and planar graphs), and also Hamiltonian graphs.[1]

An antiprism graph is a special case of a circulant graph, Ci2n (2,1).

Octahedral graph – 6 vertices, 12 edges
square antiprismatic graph – 8 vertices, 16 edges
Pentagonal antiprismatic graph – 10 vertices, 20 edges
Hexagonal antiprismatic graph – 12 vertices, 24 edges
Heptagonal antiprismatic graph – 14 vertices, 28 edges
Octagonal antiprismatic graph – 16 vertices, 32 edges
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There are also related star polygon antiprisms:

Pentagrammic antiprismatic graph – 10 vertices, 20 edges
Pentagrammic crossed-antiprismatic graph – 10 vertices, 20 edges
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Regular map (graph theory)
Archimedean graph
Prism graph
Wheel graph

References

Read, R. C. and Wilson, R. J. An Atlas of Graphs, Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 special graphs pp. 261, 270.